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-
-# 📊 Linear Programming Model — Production Optimization
-
-## ✅ Problem Statement
-
-A company, after going through a production streamlining process, ended up with the availability of 3 productive resources: **R1**, **R2**, and **R3**.
-
-A study on resource usage showed the possibility of producing two products: **P1** and **P2**. After evaluating costs and consulting the sales department, it was found that:
-
-- **P1 yields a profit of 120 monetary units per unit**
-- **P2 yields a profit of 150 monetary units per unit**
-
-The production department provided the following **resource usage** table:
-
-| Product | R1/unit | R2/unit | R3/unit |
-|---------|---------|---------|---------|
-| **P1**  |    2    |    3    |    5    |
-| **P2**  |    4    |    0    |    3    |
-
-And the **monthly resource availability**:
-
-| Resource | Monthly Availability |
-|----------|----------------------|
-| **R1**   | 100                  |
-| **R2**   | 90                   |
-| **R3**   | 120                  |
-
----
-
-## 🎯 Objective
-
-Mathematically model the **Linear Programming (LP)** problem to **maximize profit** under resource constraints.
-
----
-
-## 🧠 Step-by-Step Modeling
-
-### 1. 🧮 Decision Variables
-
-Let:
-
-x₁ = quantity produced of product P1
-x₂ = quantity produced of product P2
-
-Or in LaTeX (for use in documents):
-
-```latex
-x_1 = \text{quantity produced of product P1} \\
-x_2 = \text{quantity produced of product P2}
-
-
-
-⸻
-
-2. 📈 Objective Function
-
-Maximize total profit:
-
-\text{Maximize } Z = 120x_1 + 150x_2
-
-
-
-⸻
-
-3. 📏 Resource Constraints
-
-Each resource has limited availability:
-	•	R1 constraint:
-
-2x_1 + 4x_2 \leq 100
-
-	•	R2 constraint:
-
-3x_1 \leq 90
-
-	•	R3 constraint:
-
-5x_1 + 3x_2 \leq 120
-
-
-
-⸻
-
-4. 🚫 Non-Negativity Constraints
-
-We cannot produce a negative quantity of products:
-
-x_1 \geq 0, \quad x_2 \geq 0
-
-
-
-⸻
-
-🧾 Complete Mathematical Model
-
-\boxed{
-\begin{cases}
-\text{Maximize } Z = 120x_1 + 150x_2 \\
-2x_1 + 4x_2 \leq 100 \\
-3x_1 \leq 90 \\
-5x_1 + 3x_2 \leq 120 \\
-x_1 \geq 0, \quad x_2 \geq 0
-\end{cases}
-}
-
-
-
-⸻
-
-## 📌 Summary Tables
-
-### 🔢 Profit per Product
-
-| Product | Profit per Unit (u.m.) |
-|:--------|:----------------------:|
-| **P1**  | 120                    |
-| **P2**  | 150                    |
-
----
-
-### 🧰 Resource Usage per Unit
-
-| Product | R1/unit | R2/unit | R3/unit |
-|:--------|:-------:|:-------:|:-------:|
-| **P1**  |   2     |   3     |   5     |
-| **P2**  |   4     |   0     |   3     |
-
----
-
-### 📦 Monthly Resource Availability
-
-| Resource | Available Units |
-|:---------|:----------------:|
-| **R1**   |      100         |
-| **R2**   |       90         |
-| **R3**   |      120         |
-
-
-⸻
-
-🧠 Notes
-	•	This LP model can be solved using methods such as the Simplex Algorithm.
-	•	Can also be implemented in software such as Python (PuLP), MATLAB, or Excel Solver.
-