authors/fdabrandao/examples/quickstart.ipynb

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      "source": [
        "# amplpy setup & Quick Start\n",
        "[![quickstart.ipynb](https://img.shields.io/badge/github-%23121011.svg?logo=github)](https://github.com/ampl/colab.ampl.com/blob/master/authors/fdabrandao/examples/quickstart.ipynb) [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ampl/colab.ampl.com/blob/master/authors/fdabrandao/examples/quickstart.ipynb) [![Kaggle](https://kaggle.com/static/images/open-in-kaggle.svg)](https://kaggle.com/kernels/welcome?src=https://github.com/ampl/colab.ampl.com/blob/master/authors/fdabrandao/examples/quickstart.ipynb) [![Gradient](https://assets.paperspace.io/img/gradient-badge.svg)](https://console.paperspace.com/github/ampl/colab.ampl.com/blob/master/authors/fdabrandao/examples/quickstart.ipynb) [![Open In SageMaker Studio Lab](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/ampl/colab.ampl.com/blob/master/authors/fdabrandao/examples/quickstart.ipynb) [![Hits](https://h.ampl.com/https://github.com/ampl/colab.ampl.com/blob/master/authors/fdabrandao/examples/quickstart.ipynb)](https://colab.ampl.com)\n",
        "\n",
        "Description: amplpy setup and quick start\n",
        "\n",
        "Tags: amplpy, example\n",
        "\n",
        "Notebook author: Filipe Brandão <<fdabrandao@gmail.com>>\n",
        "\n",
        "Model author: N/A\n",
        "\n",
        "References: N/A\n",
        "\n",
        "## Setup\n",
        "\n",
        "Install from the [PiPY repository](https://pypi.python.org/pypi/amplpy):\n",
        "\n",
        "```\n",
        "$ python -m pip install amplpy\n",
        "```\n",
        "\n",
        "Note: For Windows, Linux, and macOS, the `amplpy` package comes with 33 binary wheels for Python 2.7, 3.5, 3.6, 3.7, 3.8, and 3.9. Please make sure that you are using the latest version of `pip` before installing `amplpy` (upgrade using \"`python -m pip install pip --upgrade`\"). If a binary wheel for your platform is not available, a C++ compiler and python development libraries will be required.\n",
        "\n",
        "#### Additional packages\n",
        "\n",
        "In this tutorial, we will also use [Pandas](https://pandas.pydata.org/) and [Bokeh](https://bokeh.pydata.org/). You can install these packages using \"`pip install pandas bokeh`\" or \"`python -m pip install pandas bokeh`\". Note that Bokeh is not mandatory for this tutorial.\n",
        "\n",
        "We also recommend the use of [Jupyter Notebook](https://jupyter.org/), which was used to create this tutorial. You can install Jupyter using  \"`pip install jupyter`\" or \"`python -m pip install jupyter`\"."
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      "execution_count": 95,
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        "id": "TxUsU97a4aT3",
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      "outputs": [],
      "source": [
        "# Install dependencies\n",
        "%pip install -q amplpy pandas numpy bokeh"
      ]
    },
    {
      "cell_type": "code",
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        "colab": {
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      "source": [
        "# Google Colab & Kaggle integration\n",
        "from amplpy import AMPL, ampl_notebook\n",
        "\n",
        "ampl = ampl_notebook(\n",
        "    modules=[\"gurobi\"],  # modules to install\n",
        "    license_uuid=\"default\",  # license to use\n",
        ")  # instantiate AMPL object and register magics"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kOgDX-gx4aT5"
      },
      "source": [
        "## Quick start\n",
        "\n",
        "### Step 1: Import some packages that we will use"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jj_DjQJd4aT5"
      },
      "source": [
        "Import Pandas and NumPy:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 97,
      "metadata": {
        "id": "hVhdfk844aT5"
      },
      "outputs": [],
      "source": [
        "import pandas as pd\n",
        "import numpy as np"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UxZPB0_p4aT6"
      },
      "source": [
        "Import Bokeh (do not run if you do not have Bokeh installed):"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 98,
      "metadata": {
        "id": "n1oVIhCD4aT6"
      },
      "outputs": [],
      "source": [
        "from bokeh.layouts import row\n",
        "from bokeh.plotting import figure, show"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VCV1hbs44aT6"
      },
      "source": [
        "For Jupyter Notebooks only (do not run if you are not using Bokeh and Jupyter):"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 99,
      "metadata": {
        "id": "K7KBoRYS4aT6"
      },
      "outputs": [],
      "source": [
        "from bokeh.io import output_notebook\n",
        "\n",
        "output_notebook()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4k1f7vKK4aT7"
      },
      "source": [
        "### Step 2: Import the amplpy components that we will use"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 100,
      "metadata": {
        "id": "4Yl_ZZ8E4aT7"
      },
      "outputs": [],
      "source": [
        "from amplpy import AMPL, Environment"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bfTg3gxw4aT7"
      },
      "source": [
        "### Step 3: Create an AMPL object"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 101,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "B-zovTlk4aT7",
        "outputId": "bcf5b812-d779-4346-f062-c18b255271e0"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "option version 'AMPL Development Version 20230830 (Linux-5.15.0-1042-azure, 64-bit)\\\n",
            "Licensed to AMPL Community Edition License for the AMPL Model Colaboratory (https://colab.ampl.com).\\\n",
            "Temporary license expires 20240331.\\\n",
            "Using license file \"/tmp/tmpti35nze0.lic\".\\\n",
            "';\n"
          ]
        }
      ],
      "source": [
        "ampl = AMPL()\n",
        "ampl.eval(\"option version;\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O6TQVWTn4aT8"
      },
      "source": [
        "If the AMPL installation directory is not in the system search path, you should create the AMPL object as follows instead:\n",
        "\n",
        "```python\n",
        "ampl = AMPL(Environment('full path to the AMPL installation directory'))\n",
        "```\n",
        "Note that you may need to use raw strings (e.g., `r'C:\\ampl\\ampl.mswin64'`) or escape the slashes (e.g., `'C:\\\\ampl\\\\ampl.mswin64'`) if the path includes backslashes."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o8qO56gn4aT8"
      },
      "source": [
        "### Step 4: Select the solver"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 102,
      "metadata": {
        "id": "4diKDK7s4aT8"
      },
      "outputs": [],
      "source": [
        "ampl.set_option(\"solver\", \"gurobi\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gvT04nxD4aT8"
      },
      "source": [
        "### Step 5: Define the model"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 103,
      "metadata": {
        "id": "FCWZSTNi4aT8"
      },
      "outputs": [],
      "source": [
        "ampl.eval(\n",
        "    \"\"\"\n",
        "set NUTR;\n",
        "set FOOD;\n",
        "\n",
        "param cost {FOOD} > 0;\n",
        "param f_min {FOOD} >= 0;\n",
        "param f_max {j in FOOD} >= f_min[j];\n",
        "\n",
        "param n_min {NUTR} >= 0;\n",
        "param n_max {i in NUTR} >= n_min[i];\n",
        "\n",
        "param amt {NUTR,FOOD} >= 0;\n",
        "\n",
        "var Buy {j in FOOD} >= f_min[j], <= f_max[j];\n",
        "\n",
        "minimize Total_Cost:  sum {j in FOOD} cost[j] * Buy[j];\n",
        "\n",
        "subject to Diet {i in NUTR}:\n",
        "   n_min[i] <= sum {j in FOOD} amt[i,j] * Buy[j] <= n_max[i];\n",
        "\"\"\"\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q0dXqsPA4aT8"
      },
      "source": [
        "Note: Alternatively you can read the model from a file using \"`ampl.read(filename)`\"."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KQlv83f04aT8"
      },
      "source": [
        "### Step 6: Define the initial data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 104,
      "metadata": {
        "id": "4cs9oTnP4aT8"
      },
      "outputs": [],
      "source": [
        "foods = [\"BEEF\", \"CHK\", \"FISH\", \"HAM\", \"MCH\", \"MTL\", \"SPG\", \"TUR\"]\n",
        "nutrients = [\"A\", \"C\", \"B1\", \"B2\", \"NA\", \"CAL\"]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "28hiQhwr4aT9"
      },
      "source": [
        "#### Define AMPL sets fom python lists"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 105,
      "metadata": {
        "id": "GbuY5icU4aT9"
      },
      "outputs": [],
      "source": [
        "ampl.get_set(\"FOOD\").set_values(foods)\n",
        "ampl.get_set(\"NUTR\").set_values(nutrients)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rMkKPKXF4aT9"
      },
      "source": [
        "#### Define data using an amplpy DataFrame"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 106,
      "metadata": {
        "id": "z4kqUv9N4aT9"
      },
      "outputs": [],
      "source": [
        "ampl.set_data(\n",
        "    pd.DataFrame(\n",
        "        {\n",
        "            \"cost\": [3.59, 2.59, 2.29, 2.89, 1.89, 1.99, 1.99, 2.49],\n",
        "            \"f_min\": [2, 2, 2, 2, 2, 2, 2, 2],\n",
        "            \"f_max\": [10, 10, 10, 10, 10, 10, 10, 10],\n",
        "        },\n",
        "        index=foods,\n",
        "    )\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NadzTo2m4aT9"
      },
      "source": [
        "#### Define data using a Pandas DataFrame"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 107,
      "metadata": {
        "id": "gxoiRSo34aT9",
        "scrolled": true
      },
      "outputs": [],
      "source": [
        "ampl.set_data(\n",
        "    pd.DataFrame(\n",
        "        {\n",
        "            \"n_min\": [700, 700, 700, 700, 0, 16000],\n",
        "            \"n_max\": [20000, 20000, 20000, 20000, 50000, 24000],\n",
        "        },\n",
        "        index=nutrients,\n",
        "    )\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X24aifm04aT9"
      },
      "source": [
        "#### Define data using a python dictionary"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 108,
      "metadata": {
        "id": "PAlulNOV4aT9"
      },
      "outputs": [],
      "source": [
        "ampl.get_parameter(\"amt\").set_values(\n",
        "    pd.DataFrame(\n",
        "        np.array(\n",
        "            [\n",
        "                [60, 8, 8, 40, 15, 70, 25, 60],\n",
        "                [20, 0, 10, 40, 35, 30, 50, 20],\n",
        "                [10, 20, 15, 35, 15, 15, 25, 15],\n",
        "                [15, 20, 10, 10, 15, 15, 15, 10],\n",
        "                [928, 2180, 945, 278, 1182, 896, 1329, 1397],\n",
        "                [295, 770, 440, 430, 315, 400, 379, 450],\n",
        "            ]\n",
        "        ),\n",
        "        columns=foods,\n",
        "        index=nutrients,\n",
        "    )\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-Q6uUgTG4aT-"
      },
      "source": [
        "### Step 7: Solve the model"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 109,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GLlvrNE_4aT-",
        "outputId": "c6088976-2574-4d8e-9172-2611465b9b0f"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Gurobi 10.0.2: \b\b\b\b\b\b\b\b\b\b\b\b\b\b\bGurobi 10.0.2: optimal solution; objective 119.9897589\n",
            "5 simplex iterations\n",
            " \n"
          ]
        }
      ],
      "source": [
        "ampl.solve()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w5064P_N4aT-"
      },
      "source": [
        "### Step 8: Create a Pandas DataFrame with the values of the variable 'Buy'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 110,
      "metadata": {
        "colab": {
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        "id": "uMt1Xg5m4aT-",
        "outputId": "ee0de7d4-0db8-4e14-ea2a-319a20fb3e46",
        "scrolled": true
      },
      "outputs": [
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              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-05a3d9d9-ba89-4670-9620-c033db6b0692 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "text/plain": [
              "        Buy.val\n",
              "BEEF   5.226933\n",
              "CHK    2.000000\n",
              "FISH   2.000000\n",
              "HAM   10.000000\n",
              "MCH   10.000000\n",
              "MTL   10.000000\n",
              "SPG    9.439734\n",
              "TUR    2.000000"
            ]
          },
          "execution_count": 110,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "ampl.get_variable(\"Buy\").to_pandas()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rF6F1a9G4aT-"
      },
      "source": [
        "### Step 9: Display the objective value"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 111,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fffkeJLV4aT_",
        "outputId": "54dbea47-7c1e-4e5a-d917-82e00d22164e",
        "scrolled": true
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Objective is: 119.98975893599335\n"
          ]
        }
      ],
      "source": [
        "totalcost = ampl.get_objective(\"Total_Cost\")\n",
        "print(\"Objective is:\", totalcost.value())"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MoxaWFCn4aT_"
      },
      "source": [
        "### Step 10: Increase the costs of beef and ham"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 112,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bv5EpwAu4aT_",
        "outputId": "bf9f8c31-79d2-4885-936d-dce6ed9e8f70"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Increased costs of beef and ham.\n"
          ]
        }
      ],
      "source": [
        "cost = ampl.get_parameter(\"cost\")\n",
        "cost.set_values({\"BEEF\": 5.01, \"HAM\": 4.55})\n",
        "print(\"Increased costs of beef and ham.\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yGQ40qxa4aT_"
      },
      "source": [
        "### Step 11: Solve the model with the new costs"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 113,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "767dKqCs4aUE",
        "outputId": "0ef55c8f-a787-45a1-8992-2493d144560d"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Gurobi 10.0.2: \b\b\b\b\b\b\b\b\b\b\b\b\b\b\bGurobi 10.0.2: optimal solution; objective 144.0120033\n",
            "0 simplex iterations\n",
            " \n"
          ]
        }
      ],
      "source": [
        "ampl.solve()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ROQdIH_Q4aUE"
      },
      "source": [
        "### Step 12: Display the new objective value"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 114,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uFpzGTPy4aUE",
        "outputId": "0f134435-acab-4810-b4f6-3536631058ae"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "New objective value: 144.01200332502077\n"
          ]
        }
      ],
      "source": [
        "print(\"New objective value:\", totalcost.value())"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Sak413s84aUE"
      },
      "source": [
        "### Step 13: Display the value of Buy['BEEF']"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 115,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_s266u864aUF",
        "outputId": "33ac8baa-c3e7-43f4-cdcd-970a56f788c0"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Buy['BEEF'].val = 5.226932668329175\n"
          ]
        }
      ],
      "source": [
        "Buy = ampl.get_variable(\"Buy\")\n",
        "print(\"Buy['BEEF'].val = {}\".format(Buy[\"BEEF\"].value()))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XUNNp1Kf4aUF"
      },
      "source": [
        "### Step 14: Display the dual value of each diet constraint"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 116,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vaZUH2OJ4aUF",
        "outputId": "b1c3900a-8e63-4f0c-ce31-a81b01f777bb"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Diet['A'].dual = 0.0\n",
            "Diet['C'].dual = 0.0\n",
            "Diet['B1'].dual = 0.0\n",
            "Diet['B2'].dual = 0.7999285120532004\n",
            "Diet['NA'].dual = -0.007531172069825437\n",
            "Diet['CAL'].dual = 0.0\n"
          ]
        }
      ],
      "source": [
        "diet = ampl.get_constraint(\"Diet\")\n",
        "for nutr in nutrients:\n",
        "    print(\"Diet['{}'].dual = {}\".format(nutr, diet[nutr].dual()))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IdpfYEtD4aUF"
      },
      "source": [
        "### Step 15: Display the values of the variable 'Buy' using Bokeh"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 117,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 617
        },
        "id": "hK-nRlOi4aUF",
        "outputId": "99cf8163-c6a6-45f5-e21a-8392a5d62f58"
      },
      "outputs": [
        {
          "data": {
            "application/javascript": "(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  const force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\nconst JS_MIME_TYPE = 'application/javascript';\n  const HTML_MIME_TYPE = 'text/html';\n  const EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n  const CLASS_NAME = 'output_bokeh rendered_html';\n\n  /**\n   * Render data to the DOM node\n   */\n  function render(props, node) {\n    const script = document.createElement(\"script\");\n    node.appendChild(script);\n  }\n\n  /**\n   * Handle when an output is cleared or removed\n   */\n  function handleClearOutput(event, handle) {\n    const cell = handle.cell;\n\n    const id = cell.output_area._bokeh_element_id;\n    const server_id = cell.output_area._bokeh_server_id;\n    // Clean up Bokeh references\n    if (id != null && id in Bokeh.index) {\n      Bokeh.index[id].model.document.clear();\n      delete Bokeh.index[id];\n    }\n\n    if (server_id !== undefined) {\n      // Clean up Bokeh references\n      const cmd_clean = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n      cell.notebook.kernel.execute(cmd_clean, {\n        iopub: {\n          output: function(msg) {\n            const id = msg.content.text.trim();\n            if (id in Bokeh.index) {\n              Bokeh.index[id].model.document.clear();\n              delete Bokeh.index[id];\n            }\n          }\n        }\n      });\n      // Destroy server and session\n      const cmd_destroy = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n      cell.notebook.kernel.execute(cmd_destroy);\n    }\n  }\n\n  /**\n   * Handle when a new output is added\n   */\n  function handleAddOutput(event, handle) {\n    const output_area = handle.output_area;\n    const output = handle.output;\n\n    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n    if ((output.output_type != \"display_data\") || (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n      return\n    }\n\n    const toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n\n    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n      toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n      // store reference to embed id on output_area\n      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n    }\n    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n      const bk_div = document.createElement(\"div\");\n      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n      const script_attrs = bk_div.children[0].attributes;\n      for (let i = 0; i < script_attrs.length; i++) {\n        toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n        toinsert[toinsert.length - 1].firstChild.textContent = bk_div.children[0].textContent\n      }\n      // store reference to server id on output_area\n      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n    }\n  }\n\n  function register_renderer(events, OutputArea) {\n\n    function append_mime(data, metadata, element) {\n      // create a DOM node to render to\n      const toinsert = this.create_output_subarea(\n        metadata,\n        CLASS_NAME,\n        EXEC_MIME_TYPE\n      );\n      this.keyboard_manager.register_events(toinsert);\n      // Render to node\n      const props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n      render(props, toinsert[toinsert.length - 1]);\n      element.append(toinsert);\n      return toinsert\n    }\n\n    /* Handle when an output is cleared or removed */\n    events.on('clear_output.CodeCell', handleClearOutput);\n    events.on('delete.Cell', handleClearOutput);\n\n    /* Handle when a new output is added */\n    events.on('output_added.OutputArea', handleAddOutput);\n\n    /**\n     * Register the mime type and append_mime function with output_area\n     */\n    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n      /* Is output safe? */\n      safe: true,\n      /* Index of renderer in `output_area.display_order` */\n      index: 0\n    });\n  }\n\n  // register the mime type if in Jupyter Notebook environment and previously unregistered\n  if (root.Jupyter !== undefined) {\n    const events = require('base/js/events');\n    const OutputArea = require('notebook/js/outputarea').OutputArea;\n\n    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n      register_renderer(events, OutputArea);\n    }\n  }\n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  const NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    const el = document.getElementById(null);\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error(url) {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (let i = 0; i < css_urls.length; i++) {\n      const url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error.bind(null, url);\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (let i = 0; i < js_urls.length; i++) {\n      const url = js_urls[i];\n      const element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error.bind(null, url);\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-3.2.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-3.2.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-3.2.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-3.2.2.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-3.2.2.min.js\"];\n  const css_urls = [];\n\n  const inline_js = [    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\nfunction(Bokeh) {\n    }\n  ];\n\n  function run_inline_js() {\n    if (root.Bokeh !== undefined || force === true) {\n          for (let i = 0; i < inline_js.length; i++) {\n      inline_js[i].call(root, root.Bokeh);\n    }\n} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      const cell = $(document.getElementById(null)).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));",
            "application/vnd.bokehjs_load.v0+json": ""
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"ec20db25-864d-4efe-a809-264cd4530626\" data-root-id=\"p1043\" style=\"display: contents;\"></div>\n"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
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