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    "# Problem Definition\n",
    "The company Tetravaal located in Johannesburg manufactures two types of robots, Model $P_{1}$ and Model $P_{2}$. The production plant is consisted of four different sections:  metal machining, plastic moulding, electrical work and assembly. \n",
    "The metal machining section has a capacity of 7500 units of $P_{1}$ or 6000 units of $P_{2}$ per month. \n",
    "\n",
    "\n",
    "Plastic moulding can process 5000 units of $P_{1}$ or 9000 units of $P_{2}$ per month.\n",
    "\n",
    "Electrical work can process 6000 units of $P_{1}$ or 7000 units of $P_{2}$ per month.\n",
    "\n",
    "In Assembly, there are two assembly lines that work in parallel, one per each robot model.\n",
    "\n",
    "The first assembly line can process 4000 units of $P_{1}$ per month\n",
    "\n",
    "The second assembly line can process 5000 units of $P_{2}$ per month\n",
    "\n",
    "Knowing that the unitary profit of $P_{1}$ is 500€ and that the unitary profit of $P_{2}$ is 600€, and that both robots have a great demand and therefore all manufactured robots are sold, Michelle Bradley, CEO of Tetravaal, asks his engineering team: \n",
    "\n",
    "Calculate the number of units of each robot that needs to be manufactured to maximise profit for the company."
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    "## Model\n",
    "We want to maximise the company profits:\n",
    "\n",
    "$\\max z = 500x_{1} + 600x_{2}$\n",
    "\n",
    "where z represents the profits (€). The decision variables are:\n",
    "\n",
    "$x_{1}:$ units of $P_{1}$ per month\n",
    "$x_{2}:$ units of $P_{2}$ per month\n",
    "\n",
    "The objective function is subject to the following constraints:\n",
    "\n",
    "$x_{1}/7500+x_{2}/6000 \\leq 1$ Metal machining constraint\n",
    "\n",
    "$x_{1}/5000+x_{2}/9000 \\leq 1$ Plastic moulding constraint\n",
    "\n",
    "$x_{1}/6000 + x_{2}/7000 \\leq 1$ Electrical work constraint\n",
    "\n",
    "$x_{1} \\leq 4000$ First assembly line constraint  \n",
    "\n",
    "$x_{2} \\leq 5000$ Second assembly line constraint\n",
    "\n",
    "\n",
    "\n",
    "\n"
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