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    "# Petroleum Blending\n",
    "## Problem Definition\n",
    "Harry Stamper is an engineer working on a petroleum company. The company produces three grades of motor oil – super, premium, and extra. The three grades are made from the same 3 ingredients, named component 1, component 2 and component 3. The company wants to determine the optimal mix of the 3 components in each grade of motor oil that will maximize profit. \n",
    "\n",
    "The maximum availability of each component and their cost per barrel are as follows:\n",
    "\n",
    "| Component    | Max barrels available / day  | Cost / barrel |\n",
    "|--------------|------------------------------|---------------|\n",
    "| Component 1  | 4.500                        | 12€           |\n",
    "| Component 2  | 2.700                        | 10€           |\n",
    "| Component 3  | 3.500                        | 14€           |\n",
    "\n",
    "To ensure the appropriate blend, each grade must have a minimum amount of component 1 plus a combination of other components as follows:\n",
    "\n",
    "| Grade   | Component 1  | Component 2      | Component 3       | Selling price/barrel |\n",
    "|---------|--------------|------------------|-------------------|-----------------------|\n",
    "| Super   | At least 50% | No more than 30% | -                 | 23€                   |\n",
    "| Premium | At least 40% | -                | No more than 25% | 20€                   |\n",
    "| Extra   | At least 60% | At least 10%     | -                 | 18€                   |\n",
    "\n",
    "The company wants to make at least 3000 barrels of each blend.\n",
    "*Formulate an LP to help Harry Stamper find the optimal blend that maximises profit.*"
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    "**Analysis questions**\n",
    "(Do this part once you have reviewed CLP analysis including sensitivity analysis questions). You can check the solution in the Notebook [Petroleum Blending (Solved CBC)](../solved/Petroleum%20Blending%20(Solved%20CBC).ipynb)\n",
    "\n",
    "\n",
    "* Which is the total profit obtained by the company with the Extra grade with the solution provided by the solver?\n",
    "\n",
    "\n",
    "* Which is the maximum value that the profit per barrel of component 2 in the Extra grade can take without changing the base of the optimal solution?\n",
    "\n",
    "\n",
    "* If the cost of the barrel of component 3 increased 1€, will the optimal composition change? Motivate your response\n",
    "\n",
    "\n",
    "* Do we use every barrel available of every component in the optimal solution? Or do we have any surplus availability for any component? Motivate your response\n",
    "\n",
    "\n",
    "\n",
    "* The provider of Component 2 may have a problem with the delivery and the availability may be reduced in 400 barrels. Will this shortage affect the optimal composition? Motivate your response*\n",
    "\n",
    "\n",
    "* Grace wants to use the results to renegotiate the terms and conditions with the suppliers of the different components. Which component is a better candidate to increase the availability? How would you use the model to negotiate new terms with the provider, assuming you do not want any change in the base of the optimal solution? Motivate your response"
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