Problem 4.4: MIP with piecewise linear functions (7 points) A gas company produces two types of gasoline (gas 1 and gas 2) from three types of oil (oil 1, oil 2, 0il 3). Each litre of gas 1 must contain at least 40 percent oil 1 and 20 percent of oil 2, and each litre of gas 2 must contain at least 60 percent oil 1 and 35 percent of oil 3. Each litre of gas 1 can be sold for 30 cents, and each litre of gas 2 can be sold for 40 cents. Currently, 500 litres of oil 1, 1,000 litres of oil 2 and 1,000 litres of oil 3 are available. Up to 2,000 more litres of oil 1 can be purchased at the following prices: first 250 litres at 90 cents per litre; next 250 litres at 70 cents per litre; next 500 litres at 60 cents per litre; next 1,000 litres at 40 cents per litre. (a) (1p) Let p denote the amount of additional o0il 1 that is purchased. Let (p) be the piecewise linear cost function of purchasing oil 1. Write out the piecewise linear function in the form 777 0