Please define decision variables (please include units) and develop linear program for optimum production schedule for refinery.

Please be specific about objective function and constraints.

Sunco Oil manufactures three types of gasoline (gas 1, gas 2, and gas 3). Each type of gasoline is produced by blending together three types of crude oil (crude 1, crude 2, and crude 3). The sales price per barrel of gasoline and the purchase price per barrel of crude oil are given in Table 1. Sunco can purchase up to 5000 barrels of each type of crude oil daily.

	Sales price per Barrel		Purchase Price per Barrel
Gas 1	$70	Crude 1	$45
Gas 2	$60	Crude 2	$35
Gas 3	$50	Crude 3	$25

The three types of gasoline differ in their octane ratings. The crude oil blended to form gas 1 must have an average octane rating of at least 10. The crude oil blended to form gas 2 must have an average octane rating of at least 8. The crude oil blended to form gas 3 must have an octane rating of at least 6. The octane rating of the three types of oil are given in Table 2. It costs $4 to transform one barrel of oil into one barrel of gasoline, and Suncos refinery can produce up to 14,000 barrels of gasoline daily.

Table 2. Octane Ratings.

Octane Rating

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Crude 1	12
Crude 2	6
Crude 3	8

Suncos customers require the following amounts of each gasoline: gas 13000 barrels per day; gas 22000 barrels per day; gas 31000 barrels per day. The company considers it an obligation to meet these demands