LP.ipynb

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   "source": [
    "# Part 1) A linear programming approach for optimizing features in ML models"
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    "Read the article [A linear programming approach for optimizing features in ML models](https://engineering.fb.com/2021/07/29/data-infrastructure/linear-programming/).\n",
    "\n",
    "Summarise it technically in about **400 words**, ensuring you capture the Mathematical formulation of how Linear Programming is used. (Do not discuss the code.)\n",
    "\n",
    "- Use LaTeX for the mathematical formulae, not images. You also need to expand on the formulae given in the article."
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    "## Article's summary\n",
    "\n",
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   "source": [
    "# Part 2) Farmer's Problem"
   ]
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   "source": [
    "A farmer has 500 acres of land to allocate to wheat, corn, and sugar beets.\n",
    "\n",
    "The following table summarises the requirements and constraints:\n",
    "\n",
    "|                          | Unit    | Wheat | Corn | Sugar Beets |\n",
    "|--------------------------|---------|------:|-----:|:-----------:|\n",
    "| Yield                    | T/acre  | 2.5   | 3    | 20          |\n",
    "| Demand (Need for feed)   | T       | 200   | 240  |             |\n",
    "| Planting cost            | £/acre  | 150   | 230  | 260         |\n",
    "| Selling price            | £/T     | 170   | 150  | 36 if produce ≤ 6000 T |\n",
    "|                          | £/T     |       |      | 10 if produce > 6000 T |\n",
    "| Backup (Purchase price)  | £/T     | 238   | 210  |             |"
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   "source": [
    "## Mathematical formulation"
   ]
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    "|Variable name| Description |\n",
    "|:------------|:-----|\n",
    "|$x_1$| Acres of land used for wheat |\n",
    "|$x_2$| Acres of land used for corn |\n",
    "|$x_3$| Acres of land used for sugar beets |\n",
    "|$p_1$| Tons of crop wheat sold |\n",
    "|$p_2$| Tons of crop corn sold |\n",
    "|$p_3$| Tons of crop sugar beets sold at £36 |\n",
    "|$p_4$| Tons of crop sugar beets sold at £10 |\n",
    "|$y_1$| Tons of wheat purchased |\n",
    "|$y_2$| Tons of corn purchased |"
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    "\n",
    "Profit formula:\n",
    "\n",
    "$$\n",
    ".........................\n",
    "$$"
   ]
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    "Constraints:\n",
    "\n",
    "$$\n",
    "\\begin{alignat*}{4}\n",
    "    ......................... &\\leq ...... \\\\\n",
    "    ......................... &\\leq ...... \\\\\n",
    "    ......................... \\\\\n",
    "    ......................... & \\geq 0\n",
    "\\end{alignat*}\n",
    "$$"
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   "source": [
    "## Solution using PuLP"
   ]
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   "source": [
    "from pulp import *"
   ]
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   "source": [
    "### Optimal solution\n",
    "\n",
    "|Category |Unit|Wheat|Corn|Sugar Beets|\n",
    "|---------|----|-----|----|-----------|\n",
    "|Area     |Acre|     |    |           |\n",
    "|Yield    |T   |     |    |           |\n",
    "|Sales    |T   |     |    |           |\n",
    "|Purchase |T   |     |    |           |\n",
    "\n",
    "Total cost: ..............."
   ]
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