An oil company buys fuels from large producers and sells fuels and gasolines (gasolines are mixtures of fuels) to smaller companies. The fuels properties, availability, cost and resale price are given in the following table: fuel type octane number price/barrel resale price/barrel available amount in barrels/day 4000 5050 7100 4300 86 A CON $ 31.02 $ 33.15 $ 36.35 $ 38.75 $ 36.85 $ 40.99 $ 42.95 $ 45.15 91 Three types of gasoline A, B and C are produced, with a required octane number of at least 95 (A), 90 (B) and 85 (C). Note that the octane number of a mixture is simply the weighted average over the fuels contained. The gasolines will be sold at a price of $ 45.15 (A), $ 42.95 (B) and $ 40.99 (C) per barrel. Fuels that are not used to produce gasoline will be directly sold at the resale price. (a) (7 points) Formulate a linear program for the problem of maximizing the daily profit of the oil company. Declare your variables and briefly describe your constraints. (b) (1 point) Without solving the linear program that you derived in (a), can you say how many barrels per day will be bought of each fuel type? An oil company buys fuels from large producers and sells fuels and gasolines (gasolines are mixtures of fuels) to smaller companies. The fuels properties, availability, cost and resale price are given in the following table: fuel type octane number price/barrel resale price/barrel available amount in barrels/day 4000 5050 7100 4300 86 A CON $ 31.02 $ 33.15 $ 36.35 $ 38.75 $ 36.85 $ 40.99 $ 42.95 $ 45.15 91 Three types of gasoline A, B and C are produced, with a required octane number of at least 95 (A), 90 (B) and 85 (C). Note that the octane number of a mixture is simply the weighted average over the fuels contained. The gasolines will be sold at a price of $ 45.15 (A), $ 42.95 (B) and $ 40.99 (C) per barrel. Fuels that are not used to produce gasoline will be directly sold at the resale price. (a) (7 points) Formulate a linear program for the problem of maximizing the daily profit of the oil company. Declare your variables and briefly describe your constraints. (b) (1 point) Without solving the linear program that you derived in (a), can you say how many barrels per day will be bought of each fuel type