Mixed Integer Optimization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9fc41898-5f46-4c23-a1df-2a6ffbf10495",
   "metadata": {},
   "outputs": [],
   "source": [
    "using JuMP, CSV, DataFrames, Gurobi, Interpolations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1e8f013a-b407-402f-9375-a4686aef2a5a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Read the test and train CSV files\n",
    "data_targeted = CSV.File(\"Data_Targeted.csv\") |> DataFrame;\n",
    "data_email = CSV.File(\"Data_Emails.csv\") |> DataFrame;\n",
    "data_print = CSV.File(\"Data_Print.csv\") |> DataFrame;\n",
    "data_influencer = CSV.File(\"Data_Influencers.csv\") |> DataFrame;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6dff464e-59da-41e0-ba44-9fd3e70b5c72",
   "metadata": {},
   "outputs": [],
   "source": [
    "B = [400.0, 800.0, 1000.0, 1200.0, 1500.0, 2000.0, 2500.0, 4000.0, 5000.0];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "533294d8-7a3c-4682-8639-64b5e1a96e19",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creating linear interpolation functions for each marketing option\n",
    "interp_targeted = LinearInterpolation(data_targeted[!, :Cost], data_targeted[!, :Views]);\n",
    "interp_email = LinearInterpolation(data_email[!, :Cost], data_email[!, :Views]);\n",
    "interp_print = LinearInterpolation(data_print[!, :Cost], data_print[!, :Views]);\n",
    "interp_influencers = LinearInterpolation(data_influencer[!, :Cost], data_influencer[!, :Views]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "598efdda-df58-42ec-b5f5-303e9035ebd4",
   "metadata": {},
   "source": [
    "## BASELINE "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7020c64f-c3af-4076-baf3-6f91f1058a6d",
   "metadata": {},
   "source": [
    "In summary, linear interpolation is used here to create a continuous function from your discrete data points, allowing the optimization model to work effectively with any investment amount within the provided ranges. It bridges the gap between your data and the needs of the optimization solver."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b3140c8b-c44e-4876-8b7c-9970912503fc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-10\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 25 rows, 16 columns and 48 nonzeros\n",
      "Model fingerprint: 0xae7f2303\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [2e+00, 7e+01]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 1e+03]\n",
      "Presolve removed 25 rows and 16 columns\n",
      "Presolve time: 0.00s\n",
      "Presolve: All rows and columns removed\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    1.0797713e+04   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 0 iterations and 0.00 seconds (0.00 work units)\n",
      "Optimal objective  1.079771280e+04\n",
      "\n",
      "User-callback calls 45, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = 400.0\n",
      "Targeted Online Advertising: $100.0\n",
      "Email Marketing: $100.0\n",
      "Print Media: $100.0\n",
      "Influencer Marketing: $100.0\n",
      "Total Views: 10797.7128\n",
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-10\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 25 rows, 16 columns and 48 nonzeros\n",
      "Model fingerprint: 0x8ae50363\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [2e+00, 7e+01]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 1e+03]\n",
      "Presolve removed 22 rows and 7 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 3 rows, 9 columns, 9 nonzeros\n",
      "\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    2.1598000e+04   2.552250e+01   0.000000e+00      0s\n",
      "       3    1.9274713e+04   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 3 iterations and 0.00 seconds (0.00 work units)\n",
      "Optimal objective  1.927471280e+04\n",
      "\n",
      "User-callback calls 59, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = 800.0\n",
      "Targeted Online Advertising: $200.0\n",
      "Email Marketing: $200.0\n",
      "Print Media: $200.0\n",
      "Influencer Marketing: $200.0\n",
      "Total Views: 19274.7128\n",
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-10\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 25 rows, 16 columns and 48 nonzeros\n",
      "Model fingerprint: 0x24102e8a\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [2e+00, 7e+01]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 1e+03]\n",
      "Presolve removed 22 rows and 7 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 3 rows, 9 columns, 9 nonzeros\n",
      "\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    2.6997500e+04   4.427250e+01   0.000000e+00      0s\n",
      "       3    2.2769465e+04   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 3 iterations and 0.00 seconds (0.00 work units)\n",
      "Optimal objective  2.276946530e+04\n",
      "\n",
      "User-callback calls 59, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = 1000.0\n",
      "Targeted Online Advertising: $250.0\n",
      "Email Marketing: $250.0\n",
      "Print Media: $250.0\n",
      "Influencer Marketing: $250.0\n",
      "Total Views: 22769.4653\n",
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-10\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 25 rows, 16 columns and 48 nonzeros\n",
      "Model fingerprint: 0x461d9cb5\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [2e+00, 7e+01]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 1e+03]\n",
      "Presolve removed 23 rows and 10 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 2 rows, 6 columns, 6 nonzeros\n",
      "\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    3.2237465e+04   3.400000e+01   0.000000e+00      0s\n",
      "       2    2.6219465e+04   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 2 iterations and 0.00 seconds (0.00 work units)\n",
      "Optimal objective  2.621946530e+04\n",
      "\n",
      "User-callback calls 52, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = 1200.0\n",
      "Targeted Online Advertising: $300.0\n",
      "Email Marketing: $300.0\n",
      "Print Media: $300.0\n",
      "Influencer Marketing: $300.0\n",
      "Total Views: 26219.4653\n",
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-10\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 25 rows, 16 columns and 48 nonzeros\n",
      "Model fingerprint: 0x7207260a\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [2e+00, 7e+01]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 2e+03]\n",
      "Presolve removed 23 rows and 10 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 2 rows, 6 columns, 6 nonzeros\n",
      "\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    3.8837465e+04   5.275000e+01   0.000000e+00      0s\n",
      "       2    2.8228465e+04   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 2 iterations and 0.00 seconds (0.00 work units)\n",
      "Optimal objective  2.822846530e+04\n",
      "\n",
      "User-callback calls 52, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = 1500.0\n",
      "Targeted Online Advertising: $375.0\n",
      "Email Marketing: $300.0\n",
      "Print Media: $375.0\n",
      "Influencer Marketing: $375.0\n",
      "Total Views: 28228.4653\n",
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-10\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 25 rows, 16 columns and 48 nonzeros\n",
      "Model fingerprint: 0x030f68d3\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [2e+00, 7e+01]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 2e+03]\n",
      "Presolve removed 24 rows and 13 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 1 rows, 3 columns, 3 nonzeros\n",
      "\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    3.2527465e+04   3.775000e+01   0.000000e+00      0s\n",
      "       1    3.0543465e+04   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 1 iterations and 0.00 seconds (0.00 work units)\n",
      "Optimal objective  3.054346530e+04\n",
      "\n",
      "User-callback calls 48, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = 2000.0\n",
      "Targeted Online Advertising: $500.0\n",
      "Email Marketing: $300.0\n",
      "Print Media: $495.0\n",
      "Influencer Marketing: $500.0\n",
      "Total Views: 30543.4653\n",
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-10\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 25 rows, 16 columns and 48 nonzeros\n",
      "Model fingerprint: 0x25517fa4\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [2e+00, 7e+01]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 2e+03]\n",
      "Presolve removed 25 rows and 16 columns\n",
      "Presolve time: 0.00s\n",
      "Presolve: All rows and columns removed\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    3.1356465e+04   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 0 iterations and 0.00 seconds (0.00 work units)\n",
      "Optimal objective  3.135646530e+04\n",
      "\n",
      "User-callback calls 45, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = 2500.0\n",
      "Targeted Online Advertising: $625.0\n",
      "Email Marketing: $300.0\n",
      "Print Media: $495.0\n",
      "Influencer Marketing: $594.0\n",
      "Total Views: 31356.4653\n",
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-10\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 25 rows, 16 columns and 48 nonzeros\n",
      "Model fingerprint: 0x9005ba82\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [2e+00, 7e+01]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 4e+03]\n",
      "Presolve removed 25 rows and 16 columns\n",
      "Presolve time: 0.00s\n",
      "Presolve: All rows and columns removed\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    3.2831465e+04   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 0 iterations and 0.00 seconds (0.00 work units)\n",
      "Optimal objective  3.283146530e+04\n",
      "\n",
      "User-callback calls 32, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = 4000.0\n",
      "Targeted Online Advertising: $990.0\n",
      "Email Marketing: $300.0\n",
      "Print Media: $495.0\n",
      "Influencer Marketing: $594.0\n",
      "Total Views: 32831.465299999996\n",
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-10\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 25 rows, 16 columns and 48 nonzeros\n",
      "Model fingerprint: 0x7a64fe30\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+00]\n",
      "  Objective range  [2e+00, 7e+01]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 5e+03]\n",
      "Presolve removed 25 rows and 16 columns\n",
      "Presolve time: 0.00s\n",
      "Presolve: All rows and columns removed\n",
      "Iteration    Objective       Primal Inf.    Dual Inf.      Time\n",
      "       0    3.2831465e+04   0.000000e+00   0.000000e+00      0s\n",
      "\n",
      "Solved in 0 iterations and 0.00 seconds (0.00 work units)\n",
      "Optimal objective  3.283146530e+04\n",
      "\n",
      "User-callback calls 32, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = 5000.0\n",
      "Targeted Online Advertising: $990.0\n",
      "Email Marketing: $300.0\n",
      "Print Media: $495.0\n",
      "Influencer Marketing: $594.0\n",
      "Total Views: 32831.465299999996\n"
     ]
    }
   ],
   "source": [
    "for Budget in B\n",
    "        # Optimization model\n",
    "        model = Model(Gurobi.Optimizer)\n",
    "        \n",
    "        # Decision variables for investments\n",
    "        @variable(model, investment_targeted >= 0)\n",
    "        @variable(model, investment_email >= 0)\n",
    "        @variable(model, investment_print >= 0)\n",
    "        @variable(model, investment_influencers >= 0)\n",
    "        \n",
    "        # Additional variables and constraints for piecewise linear segments for each marketing option\n",
    "        # Helps in modeling non-linear relationships\n",
    "        \n",
    "        # Creating a piecewise linear function\n",
    "        # Targeted Online Advertising\n",
    "        @variable(model, targeted_segments[1:3] >= 0) #each col is non-negative\n",
    "        \n",
    "        breakpoints_targeted = [0, 40, 310, 990] \n",
    "        # Example breakpoints \n",
    "        #defines the investment levels at which the slope (rate of increase in views) changes. \n",
    "        #These breakpoints divide the investment range into segments.\n",
    "        \n",
    "        slopes_targeted = [3, 4, 5] \n",
    "        # Example slopes\n",
    "        # represents the rate of change in views per unit of investment in each segment. For instance, a slope of 0.8 for the \n",
    "        #first segment means that for each unit of investment in this segment, the views increase by 0.8.\n",
    "        \n",
    "        @constraint(model, investment_targeted == sum(targeted_segments)) #the sum of investments across all segments\n",
    "        \n",
    "        @constraint(model, sum(targeted_segments[i] for i in 1:3) <= breakpoints_targeted[end])\n",
    "        for i in 1:3\n",
    "            @constraint(model, targeted_segments[i] <= breakpoints_targeted[i+1] - breakpoints_targeted[i])\n",
    "        end\n",
    "        \n",
    "        # Email Marketing - done\n",
    "        # Example breakpoints and slopes for Email Marketing\n",
    "        @variable(model, email_segments[1:3] >= 0) \n",
    "        breakpoints_email = [0, 77.05, 144.87, 300] # Example breakpoints \n",
    "        slopes_email = [18, 19.99, 19.95] # Example slopes\n",
    "        @constraint(model, investment_email == sum(email_segments))\n",
    "        @constraint(model, sum(email_segments[i] for i in 1:3) <= breakpoints_email[end])\n",
    "        for i in 1:3\n",
    "            @constraint(model, email_segments[i] <= breakpoints_email[i+1] - breakpoints_email[i])\n",
    "        end\n",
    "        \n",
    "        # Print Media - done\n",
    "        # Example breakpoints and slopes for Print Media\n",
    "        @variable(model, print_segments[1:3] >= 0)\n",
    "        slopes_print = [12, 40, 73] # Example breakpoints\n",
    "        breakpoints_print = [200, 375, 565, 695] # Example slopes\n",
    "        @constraint(model, investment_print == sum(print_segments))\n",
    "        @constraint(model, sum(print_segments[i] for i in 1:3) <= breakpoints_print[end])\n",
    "        for i in 1:3\n",
    "            @constraint(model, print_segments[i] <= breakpoints_print[i+1] - breakpoints_print[i])\n",
    "        end\n",
    "        \n",
    "        # Influencer Marketing - done\n",
    "        # Example breakpoints and slopes for Influencer Marketing\n",
    "        @variable(model, influencers_segments[1:3] >= 0)\n",
    "        breakpoints_influencers = [100, 298, 406, 694] # Example breakpoints\n",
    "        slopes_influencers = [10, 6, 2] # Example slopes\n",
    "        @constraint(model, investment_influencers == sum(influencers_segments))\n",
    "        @constraint(model, sum(influencers_segments[i] for i in 1:3) <= breakpoints_influencers[end])\n",
    "        for i in 1:3\n",
    "            @constraint(model, influencers_segments[i] <= breakpoints_influencers[i+1] - breakpoints_influencers[i])\n",
    "        end\n",
    "        \n",
    "        # Objective: Maximize views\n",
    "        @objective(model, Max, sum(slopes_targeted[i] * targeted_segments[i] for i in eachindex(slopes_targeted)) + \n",
    "                      sum(slopes_email[i] * email_segments[i] for i in eachindex(slopes_email)) +\n",
    "                      sum(slopes_print[i] * print_segments[i] for i in eachindex(slopes_print)) +\n",
    "                      sum(slopes_influencers[i] * influencers_segments[i] for i in eachindex(slopes_influencers)))\n",
    "\n",
    "        \n",
    "        # Budget constraint\n",
    "            @constraint(model, investment_targeted + investment_email +\n",
    "                           investment_print + investment_influencers <= Budget)\n",
    "\n",
    "        # Baseline constraints\n",
    "        @constraint(model, investment_targeted <= Budget/4)\n",
    "        @constraint(model, investment_email <= Budget/4)\n",
    "        @constraint(model, investment_print <= Budget/4)\n",
    "        @constraint(model, investment_influencers <= Budget/4)\n",
    "        \n",
    "        # Solve the model\n",
    "        optimize!(model)\n",
    "        \n",
    "        # Results\n",
    "        println(\"Optimal Investments with Budget = \", Budget)\n",
    "        println(\"Targeted Online Advertising: \\$\", value(investment_targeted))\n",
    "        println(\"Email Marketing: \\$\", value(investment_email))\n",
    "        println(\"Print Media: \\$\", value(investment_print))\n",
    "        println(\"Influencer Marketing: \\$\", value(investment_influencers))\n",
    "        println(\"Total Views: \", objective_value(model))\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58a5bf22-12c5-4c3f-9783-80d2849535b6",
   "metadata": {},
   "source": [
    "## MIO "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1d5de72c-afd7-487e-b142-062917389999",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10000"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BigM = 10000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1d7c2407-fda8-4519-9c12-e1e70227713e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-10\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 25 rows, 20 columns and 56 nonzeros\n",
      "Model fingerprint: 0x7df6bd8f\n",
      "Variable types: 16 continuous, 4 integer (4 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+04]\n",
      "  Objective range  [2e+00, 7e+01]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 1e+03]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 20 rows and 6 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 5 rows, 14 columns, 28 nonzeros\n",
      "Variable types: 10 continuous, 4 integer (4 binary)\n",
      "\n",
      "Root relaxation: objective 1.495667e+04, 2 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0 14956.6667    0    1   -0.00000 14956.6667      -     -    0s\n",
      "H    0     0                    12290.000000 14956.6667  21.7%     -    0s\n",
      "\n",
      "Explored 1 nodes (2 simplex iterations) in 0.00 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 2: 12290 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 1.229000000000e+04, best bound 1.229000000000e+04, gap 0.0000%\n",
      "\n",
      "User-callback calls 284, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = 400.0\n",
      "Targeted Online Advertising: $0.0\n",
      "Email Marketing: $0.0\n",
      "Print Media: $199.99999999999994\n",
      "Influencer Marketing: $0.0\n",
      "Total Views: 12289.999999999998\n",
      "Investments with onboarding fees:\n",
      "Print Media: $199.99999999999994 (Onboarding Fee Paid)\n",
      "Email Marketing: $0.0\n",
      "Influencer Marketing: $0.0\n",
      "Targeted Online Advertising: $0.0\n",
      "Total Onboarding Fees Paid: $200\n",
      "Total Investment Amount: $199.99999999999994\n",
      "Total Views: 12289.999999999998\n",
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-10\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 25 rows, 20 columns and 56 nonzeros\n",
      "Model fingerprint: 0x98c10972\n",
      "Variable types: 16 continuous, 4 integer (4 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+04]\n",
      "  Objective range  [2e+00, 7e+01]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 1e+03]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 20 rows and 4 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 5 rows, 16 columns, 32 nonzeros\n",
      "Variable types: 12 continuous, 4 integer (4 binary)\n",
      "\n",
      "Root relaxation: objective 2.129068e+04, 4 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0 21290.6764    0    2   -0.00000 21290.6764      -     -    0s\n",
      "H    0     0                    16073.706739 21290.6764  32.5%     -    0s\n",
      "H    0     0                    18688.712800 21290.6764  13.9%     -    0s\n",
      "H    0     0                    19190.000000 20357.3297  6.08%     -    0s\n",
      "     0     0 19190.0000    0    1 19190.0000 19190.0000  0.00%     -    0s\n",
      "\n",
      "Cutting planes:\n",
      "  Gomory: 1\n",
      "  Implied bound: 2\n",
      "  RLT: 1\n",
      "\n",
      "Explored 1 nodes (7 simplex iterations) in 0.00 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 3: 19190 18688.7 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 1.919000000000e+04, best bound 1.919000000000e+04, gap 0.0000%\n",
      "\n",
      "User-callback calls 256, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = 800.0\n",
      "Targeted Online Advertising: $0.0\n",
      "Email Marketing: $0.0\n",
      "Print Media: $495.0\n",
      "Influencer Marketing: $0.0\n",
      "Total Views: 19190.0\n",
      "Investments with onboarding fees:\n",
      "Print Media: $495.0 (Onboarding Fee Paid)\n",
      "Email Marketing: $0.0\n",
      "Influencer Marketing: $0.0\n",
      "Targeted Online Advertising: $0.0\n",
      "Total Onboarding Fees Paid: $200\n",
      "Total Investment Amount: $495.0\n",
      "Total Views: 19190.0\n",
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-10\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 25 rows, 20 columns and 56 nonzeros\n",
      "Model fingerprint: 0x457a03f7\n",
      "Variable types: 16 continuous, 4 integer (4 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+04]\n",
      "  Objective range  [2e+00, 7e+01]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 1e+03]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 20 rows and 4 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 5 rows, 16 columns, 32 nonzeros\n",
      "Variable types: 12 continuous, 4 integer (4 binary)\n",
      "\n",
      "Root relaxation: objective 2.336085e+04, 5 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0 23360.8466    0    1   -0.00000 23360.8466      -     -    0s\n",
      "H    0     0                    21116.242278 23360.8466  10.6%     -    0s\n",
      "H    0     0                    22241.350192 23360.8466  5.03%     -    0s\n",
      "H    0     0                    22567.465300 22567.4653  0.00%     -    0s\n",
      "     0     0          -    0      22567.4653 22567.4653  0.00%     -    0s\n",
      "\n",
      "Cutting planes:\n",
      "  Relax-and-lift: 1\n",
      "\n",
      "Explored 1 nodes (9 simplex iterations) in 0.00 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 2: 22567.5 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 2.256746530000e+04, best bound 2.256746530000e+04, gap 0.0000%\n",
      "\n",
      "User-callback calls 253, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = 1000.0\n",
      "Targeted Online Advertising: $0.0\n",
      "Email Marketing: $279.99999999999994\n",
      "Print Media: $320.0\n",
      "Influencer Marketing: $0.0\n",
      "Total Views: 22567.4653\n",
      "Investments with onboarding fees:\n",
      "Print Media: $320.0 (Onboarding Fee Paid)\n",
      "Email Marketing: $279.99999999999994 (Onboarding Fee Paid)\n",
      "Influencer Marketing: $0.0\n",
      "Targeted Online Advertising: $0.0\n",
      "Total Onboarding Fees Paid: $400\n",
      "Total Investment Amount: $600.0\n",
      "Total Views: 22567.4653\n",
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-10\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 25 rows, 20 columns and 56 nonzeros\n",
      "Model fingerprint: 0xdb2b7b6a\n",
      "Variable types: 16 continuous, 4 integer (4 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+04]\n",
      "  Objective range  [2e+00, 7e+01]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 1e+03]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 20 rows and 4 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 5 rows, 16 columns, 32 nonzeros\n",
      "Variable types: 12 continuous, 4 integer (4 binary)\n",
      "\n",
      "Root relaxation: objective 2.506487e+04, 6 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0 25064.8708    0    1   -0.00000 25064.8708      -     -    0s\n",
      "H    0     0                    17367.465300 25064.8708  44.3%     -    0s\n",
      "H    0     0                    25027.465300 25064.8708  0.15%     -    0s\n",
      "     0     0 25064.8708    0    1 25027.4653 25064.8708  0.15%     -    0s\n",
      "\n",
      "Explored 1 nodes (6 simplex iterations) in 0.00 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 3: 25027.5 17367.5 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 2.502746530000e+04, best bound 2.502746530000e+04, gap 0.0000%\n",
      "\n",
      "User-callback calls 246, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = 1200.0\n",
      "Targeted Online Advertising: $0.0\n",
      "Email Marketing: $300.0\n",
      "Print Media: $495.0\n",
      "Influencer Marketing: $0.0\n",
      "Total Views: 25027.4653\n",
      "Investments with onboarding fees:\n",
      "Print Media: $495.0 (Onboarding Fee Paid)\n",
      "Email Marketing: $300.0 (Onboarding Fee Paid)\n",
      "Influencer Marketing: $0.0\n",
      "Targeted Online Advertising: $0.0\n",
      "Total Onboarding Fees Paid: $400\n",
      "Total Investment Amount: $795.0\n",
      "Total Views: 25027.4653\n",
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-10\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 25 rows, 20 columns and 56 nonzeros\n",
      "Model fingerprint: 0x51922b3c\n",
      "Variable types: 16 continuous, 4 integer (4 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+04]\n",
      "  Objective range  [2e+00, 7e+01]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 2e+03]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 20 rows and 4 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 5 rows, 16 columns, 32 nonzeros\n",
      "Variable types: 12 continuous, 4 integer (4 binary)\n",
      "\n",
      "Root relaxation: objective 2.718851e+04, 5 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0 27188.5081    0    1   -0.00000 27188.5081      -     -    0s\n",
      "H    0     0                    25956.770086 27188.5081  4.75%     -    0s\n",
      "H    0     0                    26077.465300 27188.5081  4.26%     -    0s\n",
      "\n",
      "Cutting planes:\n",
      "  Gomory: 1\n",
      "  Implied bound: 1\n",
      "  Flow cover: 1\n",
      "\n",
      "Explored 1 nodes (5 simplex iterations) in 0.00 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 2: 26077.5 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 2.607746530000e+04, best bound 2.607746530000e+04, gap 0.0000%\n",
      "\n",
      "User-callback calls 250, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = 1500.0\n",
      "Targeted Online Advertising: $0.0\n",
      "Email Marketing: $300.0\n",
      "Print Media: $495.0\n",
      "Influencer Marketing: $105.00000000000014\n",
      "Total Views: 26077.4653\n",
      "Investments with onboarding fees:\n",
      "Print Media: $495.0 (Onboarding Fee Paid)\n",
      "Email Marketing: $300.0 (Onboarding Fee Paid)\n",
      "Influencer Marketing: $105.00000000000014 (Onboarding Fee Paid)\n",
      "Targeted Online Advertising: $0.0\n",
      "Total Onboarding Fees Paid: $600\n",
      "Total Investment Amount: $900.0000000000001\n",
      "Total Views: 26077.4653\n",
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-10\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 25 rows, 20 columns and 56 nonzeros\n",
      "Model fingerprint: 0x34722661\n",
      "Variable types: 16 continuous, 4 integer (4 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+04]\n",
      "  Objective range  [2e+00, 7e+01]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 2e+03]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 20 rows and 4 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 5 rows, 16 columns, 32 nonzeros\n",
      "Variable types: 12 continuous, 4 integer (4 binary)\n",
      "\n",
      "Root relaxation: objective 2.927175e+04, 6 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0 29271.7503    0    2   -0.00000 29271.7503      -     -    0s\n",
      "H    0     0                    28150.465300 29271.7503  3.98%     -    0s\n",
      "H    0     0                    28231.465300 29271.7503  3.68%     -    0s\n",
      "\n",
      "Cutting planes:\n",
      "  Gomory: 1\n",
      "  Relax-and-lift: 1\n",
      "\n",
      "Explored 1 nodes (6 simplex iterations) in 0.00 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 3: 28231.5 28150.5 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 2.823146530000e+04, best bound 2.823146530000e+04, gap 0.0000%\n",
      "\n",
      "User-callback calls 313, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = 2000.0\n",
      "Targeted Online Advertising: $0.0\n",
      "Email Marketing: $300.0\n",
      "Print Media: $495.0\n",
      "Influencer Marketing: $594.0\n",
      "Total Views: 28231.4653\n",
      "Investments with onboarding fees:\n",
      "Print Media: $495.0 (Onboarding Fee Paid)\n",
      "Email Marketing: $300.0 (Onboarding Fee Paid)\n",
      "Influencer Marketing: $594.0 (Onboarding Fee Paid)\n",
      "Targeted Online Advertising: $0.0\n",
      "Total Onboarding Fees Paid: $600\n",
      "Total Investment Amount: $1389.0\n",
      "Total Views: 28231.4653\n",
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-10\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 25 rows, 20 columns and 56 nonzeros\n",
      "Model fingerprint: 0x40d8aa61\n",
      "Variable types: 16 continuous, 4 integer (4 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+04]\n",
      "  Objective range  [2e+00, 7e+01]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 2e+03]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 21 rows and 5 columns\n",
      "Presolve time: 0.00s\n",
      "Presolved: 4 rows, 15 columns, 27 nonzeros\n",
      "Found heuristic solution: objective 5.0000000\n",
      "Variable types: 12 continuous, 3 integer (3 binary)\n",
      "\n",
      "Root relaxation: objective 3.085653e+04, 6 iterations, 0.00 seconds (0.00 work units)\n",
      "\n",
      "    Nodes    |    Current Node    |     Objective Bounds      |     Work\n",
      " Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time\n",
      "\n",
      "     0     0 30856.5259    0    1    5.00000 30856.5259      -     -    0s\n",
      "H    0     0                    30650.465300 30856.5259  0.67%     -    0s\n",
      "\n",
      "Explored 1 nodes (6 simplex iterations) in 0.00 seconds (0.00 work units)\n",
      "Thread count was 8 (of 8 available processors)\n",
      "\n",
      "Solution count 3: 30650.5 5 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 3.065046530000e+04, best bound 3.065046530000e+04, gap 0.0000%\n",
      "\n",
      "User-callback calls 362, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = 2500.0\n",
      "Targeted Online Advertising: $599.0000000000001\n",
      "Email Marketing: $300.0\n",
      "Print Media: $495.0\n",
      "Influencer Marketing: $306.0\n",
      "Total Views: 30650.4653\n",
      "Investments with onboarding fees:\n",
      "Print Media: $495.0 (Onboarding Fee Paid)\n",
      "Email Marketing: $300.0 (Onboarding Fee Paid)\n",
      "Influencer Marketing: $306.0 (Onboarding Fee Paid)\n",
      "Targeted Online Advertising: $599.0000000000001 (Onboarding Fee Paid)\n",
      "Total Onboarding Fees Paid: $800\n",
      "Total Investment Amount: $1700.0\n",
      "Total Views: 30650.4653\n",
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-10\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 25 rows, 20 columns and 56 nonzeros\n",
      "Model fingerprint: 0x7355275b\n",
      "Variable types: 16 continuous, 4 integer (4 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+04]\n",
      "  Objective range  [2e+00, 7e+01]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 4e+03]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 25 rows and 20 columns\n",
      "Presolve time: 0.00s\n",
      "Presolve: All rows and columns removed\n",
      "\n",
      "Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)\n",
      "Thread count was 1 (of 8 available processors)\n",
      "\n",
      "Solution count 2: 32831.5 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 3.283146530000e+04, best bound 3.283146530000e+04, gap 0.0000%\n",
      "\n",
      "User-callback calls 191, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = 4000.0\n",
      "Targeted Online Advertising: $990.0\n",
      "Email Marketing: $300.0\n",
      "Print Media: $495.0\n",
      "Influencer Marketing: $594.0\n",
      "Total Views: 32831.465299999996\n",
      "Investments with onboarding fees:\n",
      "Print Media: $495.0 (Onboarding Fee Paid)\n",
      "Email Marketing: $300.0 (Onboarding Fee Paid)\n",
      "Influencer Marketing: $594.0 (Onboarding Fee Paid)\n",
      "Targeted Online Advertising: $990.0 (Onboarding Fee Paid)\n",
      "Total Onboarding Fees Paid: $800\n",
      "Total Investment Amount: $2379.0\n",
      "Total Views: 32831.465299999996\n",
      "Set parameter Username\n",
      "Academic license - for non-commercial use only - expires 2024-09-10\n",
      "Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])\n",
      "\n",
      "CPU model: Apple M2\n",
      "Thread count: 8 physical cores, 8 logical processors, using up to 8 threads\n",
      "\n",
      "Optimize a model with 25 rows, 20 columns and 56 nonzeros\n",
      "Model fingerprint: 0x55307718\n",
      "Variable types: 16 continuous, 4 integer (4 binary)\n",
      "Coefficient statistics:\n",
      "  Matrix range     [1e+00, 1e+04]\n",
      "  Objective range  [2e+00, 7e+01]\n",
      "  Bounds range     [0e+00, 0e+00]\n",
      "  RHS range        [4e+01, 5e+03]\n",
      "Found heuristic solution: objective -0.0000000\n",
      "Presolve removed 25 rows and 20 columns\n",
      "Presolve time: 0.00s\n",
      "Presolve: All rows and columns removed\n",
      "\n",
      "Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)\n",
      "Thread count was 1 (of 8 available processors)\n",
      "\n",
      "Solution count 2: 32831.5 -0 \n",
      "\n",
      "Optimal solution found (tolerance 1.00e-04)\n",
      "Best objective 3.283146530000e+04, best bound 3.283146530000e+04, gap 0.0000%\n",
      "\n",
      "User-callback calls 191, time in user-callback 0.00 sec\n",
      "Optimal Investments with Budget = 5000.0\n",
      "Targeted Online Advertising: $990.0\n",
      "Email Marketing: $300.0\n",
      "Print Media: $495.0\n",
      "Influencer Marketing: $594.0\n",
      "Total Views: 32831.465299999996\n",
      "Investments with onboarding fees:\n",
      "Print Media: $495.0 (Onboarding Fee Paid)\n",
      "Email Marketing: $300.0 (Onboarding Fee Paid)\n",
      "Influencer Marketing: $594.0 (Onboarding Fee Paid)\n",
      "Targeted Online Advertising: $990.0 (Onboarding Fee Paid)\n",
      "Total Onboarding Fees Paid: $800\n",
      "Total Investment Amount: $2379.0\n",
      "Total Views: 32831.465299999996\n"
     ]
    }
   ],
   "source": [
    "for Budget in B\n",
    "        # Optimization model\n",
    "        model = Model(Gurobi.Optimizer)\n",
    "        \n",
    "       # Decision variables for investments\n",
    "        @variable(model, investment_targeted >= 0)\n",
    "        @variable(model, investment_email >= 0)\n",
    "        @variable(model, investment_print >= 0)\n",
    "        @variable(model, investment_influencers >= 0)\n",
    "        \n",
    "        # Binary variables for onboarding fee\n",
    "        @variable(model, onboard_targeted, Bin)\n",
    "        @variable(model, onboard_email, Bin)\n",
    "        @variable(model, onboard_print, Bin)\n",
    "        @variable(model, onboard_influencers, Bin)\n",
    "        \n",
    "        # Onboarding fee constraints\n",
    "        @constraint(model, investment_targeted <= onboard_targeted * BigM)\n",
    "        @constraint(model, investment_email <= onboard_email * BigM)\n",
    "        @constraint(model, investment_print <= onboard_print * BigM)\n",
    "        @constraint(model, investment_influencers <= onboard_influencers * BigM)\n",
    "\n",
    "        # Additional variables and constraints for piecewise linear segments for each marketing option\n",
    "        # Helps in modeling non-linear relationships\n",
    "        \n",
    "        # Creating a piecewise linear function\n",
    "        # Targeted Online Advertising\n",
    "        @variable(model, targeted_segments[1:3] >= 0) #each col is non-negative\n",
    "        \n",
    "        breakpoints_targeted = [0, 40, 310, 990] \n",
    "        # Example breakpoints \n",
    "        #defines the investment levels at which the slope (rate of increase in views) changes. \n",
    "        #These breakpoints divide the investment range into segments.\n",
    "        \n",
    "        slopes_targeted = [3, 4, 5] \n",
    "        # Example slopes\n",
    "        # represents the rate of change in views per unit of investment in each segment. For instance, a slope of 0.8 for the \n",
    "        #first segment means that for each unit of investment in this segment, the views increase by 0.8.\n",
    "        \n",
    "        @constraint(model, investment_targeted == sum(targeted_segments)) #the sum of investments across all segments\n",
    "        \n",
    "        @constraint(model, sum(targeted_segments[i] for i in 1:3) <= breakpoints_targeted[end])\n",
    "        for i in 1:3\n",
    "            @constraint(model, targeted_segments[i] <= breakpoints_targeted[i+1] - breakpoints_targeted[i])\n",
    "        end\n",
    "        \n",
    "        # Email Marketing - done\n",
    "        # Example breakpoints and slopes for Email Marketing\n",
    "        @variable(model, email_segments[1:3] >= 0) \n",
    "        breakpoints_email = [0, 77.05, 144.87, 300] # Example breakpoints \n",
    "        slopes_email = [18, 19.99, 19.95] # Example slopes\n",
    "        @constraint(model, investment_email == sum(email_segments))\n",
    "        @constraint(model, sum(email_segments[i] for i in 1:3) <= breakpoints_email[end])\n",
    "        for i in 1:3\n",
    "            @constraint(model, email_segments[i] <= breakpoints_email[i+1] - breakpoints_email[i])\n",
    "        end\n",
    "        \n",
    "        # Print Media - done\n",
    "        # Example breakpoints and slopes for Print Media\n",
    "        @variable(model, print_segments[1:3] >= 0)\n",
    "        slopes_print = [12, 40, 73] # Example breakpoints\n",
    "        breakpoints_print = [200, 375, 565, 695] # Example slopes\n",
    "        @constraint(model, investment_print == sum(print_segments))\n",
    "        @constraint(model, sum(print_segments[i] for i in 1:3) <= breakpoints_print[end])\n",
    "        for i in 1:3\n",
    "            @constraint(model, print_segments[i] <= breakpoints_print[i+1] - breakpoints_print[i])\n",
    "        end\n",
    "        \n",
    "        # Influencer Marketing - done\n",
    "        # Example breakpoints and slopes for Influencer Marketing\n",
    "        @variable(model, influencers_segments[1:3] >= 0)\n",
    "        breakpoints_influencers = [100, 298, 406, 694] # Example breakpoints\n",
    "        slopes_influencers = [10, 6, 2] # Example slopes\n",
    "        @constraint(model, investment_influencers == sum(influencers_segments))\n",
    "        @constraint(model, sum(influencers_segments[i] for i in 1:3) <= breakpoints_influencers[end])\n",
    "        for i in 1:3\n",
    "            @constraint(model, influencers_segments[i] <= breakpoints_influencers[i+1] - breakpoints_influencers[i])\n",
    "        end\n",
    "        \n",
    "        # Objective: Maximize views\n",
    "        @objective(model, Max, sum(slopes_targeted[i] * targeted_segments[i] for i in eachindex(slopes_targeted)) + \n",
    "                      sum(slopes_email[i] * email_segments[i] for i in eachindex(slopes_email)) +\n",
    "                      sum(slopes_print[i] * print_segments[i] for i in eachindex(slopes_print)) +\n",
    "                      sum(slopes_influencers[i] * influencers_segments[i] for i in eachindex(slopes_influencers)))\n",
    "    \n",
    "        # Budget constraint\n",
    "            @constraint(model, investment_targeted + investment_email +\n",
    "                           investment_print + investment_influencers + \n",
    "            200*(onboard_targeted + onboard_email + onboard_print + onboard_influencers) <= Budget)\n",
    "        # Solve the model\n",
    "        optimize!(model)\n",
    "        \n",
    "        # Results\n",
    "        println(\"Optimal Investments with Budget = \", Budget)\n",
    "        println(\"Targeted Online Advertising: \\$\", value(investment_targeted))\n",
    "        println(\"Email Marketing: \\$\", value(investment_email))\n",
    "        println(\"Print Media: \\$\", value(investment_print))\n",
    "        println(\"Influencer Marketing: \\$\", value(investment_influencers))\n",
    "        println(\"Total Views: \", objective_value(model))\n",
    "\n",
    "        # Check which investments have been made and calculate onboarding fees\n",
    "        onboarding_fees_paid = 0\n",
    "        total_investment = 0\n",
    "        \n",
    "        # Create a dictionary to map the investment decision variables to their names and binary onboarding variables\n",
    "        investments = Dict(\n",
    "            \"Targeted Online Advertising\" => (investment_targeted, onboard_targeted),\n",
    "            \"Email Marketing\" => (investment_email, onboard_email),\n",
    "            \"Print Media\" => (investment_print, onboard_print),\n",
    "            \"Influencer Marketing\" => (investment_influencers, onboard_influencers)\n",
    "        )\n",
    "        \n",
    "        println(\"Investments with onboarding fees:\")\n",
    "        for (name, (invest_var, onboard_var)) in investments\n",
    "            invest_value = value(invest_var)\n",
    "            onboard_value = value(onboard_var)\n",
    "            total_investment += invest_value\n",
    "            if onboard_value == 1\n",
    "                onboarding_fees_paid += 200\n",
    "                println(\"$name: \\$\", invest_value, \" (Onboarding Fee Paid)\")\n",
    "            else\n",
    "                println(\"$name: \\$\", invest_value)\n",
    "            end\n",
    "        end\n",
    "        \n",
    "        println(\"Total Onboarding Fees Paid: \\$\", onboarding_fees_paid)\n",
    "        println(\"Total Investment Amount: \\$\", total_investment)\n",
    "        println(\"Total Views: \", objective_value(model))\n",
    "end"
   ]
  },
  {
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   "id": "cb61c46c-b7c0-401f-a155-1b1cfc9f2b19",
   "metadata": {},
   "outputs": [],
   "source": []
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