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    "# Making Weapons\n",
    "## Problem Definition\n",
    "Din Djarin is a retired bounty hunter that now runs a small factory specialised in making classic weapons in a colony recently re-established in Mandalore. The factory manufactures two different types of weapons, swords and spears. Din uses special alloys, mixtures of metals and rare materials, which have made a name for the endurance of his weapons across the colony. The table below shows the weight in pounds of each material needed to make each type of weapon:\n",
    "\n",
    "| Metal    | spear | sword |\n",
    "|----------|-------|-------|\n",
    "| Beskar   |   1   |  0.5  |\n",
    "| Tungsten |   1   |   1   |\n",
    "| Titanium |   3   |   1   |\n",
    "\n",
    "And the table below shows the total amount of each metal available, also in pounds: \n",
    "\n",
    "| Metal    | Amount |\n",
    "|----------|--------|\n",
    "|  Beskar  |  125   |\n",
    "| Tungsten |  225   |\n",
    "| Titanium |  300   |\n",
    "\n",
    "The price of a spade is 40 credits and the price of a sword is 5 credits. Din has already sold 100 swords, so he needs to manufacture at least that many. \n",
    "\n",
    "**Find the optimal number of spades and swords that maximise revenues**"
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    "## Model"
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    "The objective is to maximise the revenues obtained with the sales of both types of weapons. \n",
    "The objective function can be modeled as:\n",
    "\n",
    "$\\max z = 40x_{1} + 5x_{2}$\n",
    "\n",
    "where z represents the objective variable (profits) and the decision variables are:\n",
    "\n",
    "\n",
    "- $x_{1}$: units of spears\n",
    "\n",
    "- $x_{2}$: units of swords\n",
    "\n",
    "Let us for now consider that they are real and non-negative. \n",
    "\n",
    "The objective function is subject to the following constraints:\n",
    "\n",
    "Metal availability constraints: \n",
    "\n",
    "$x_{1} + 0.5x_{2} \\leq 125$\n",
    "\n",
    "$x_{1} + x_{2} \\leq 225$\n",
    "\n",
    "$3x_{1} + x_{2} \\leq 300$\n",
    "\n",
    "And the demand on swords:\n",
    "\n",
    "$x_{2} \\geq 100$\n",
    "\n",
    " \n"
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