1) Sunco Oil manufactures three types of gasoline (Gas1, Gas 2, and Gas 3). Each type is produced by blending 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 5,000 barrels of each type of crude oil daily The three types of gasoline differ in their octane rating and sulfur content. The crude oil blended to form Gas I must have an average octane rating of at least 10 and contain at most 1% sulfur. The crude oil blended to form Gas 2 must have an average octane rating of at least 8 and contain at most 2% sulfur. The crude oil blended to form Gas 3 must have an octane rating of at least 6 and contain at most 1% sulfur. The octane rating and the sulfur content 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 Sunco's refinery can produce up to 14,000 barrels of gasoline daily Sunco's customers require the following amounts of each gasoline: Gas 3,000 barrels per day Gas 2 2,000 barrels per day, Gas 3 1,000 barrels per day. The company considers it an obligation to meet these demands. Sunco also has the option of advertising to stimulate demand for its products. Each dollar spent daily in advertising a particular type of gas increases the daily demand for that type of gas by 10 barrels. For example, if Sunco decides to spend S20 daily in advertising Gas 2, then the daily demand for Gas 2 will increase by 20 x 10 200 barrels a) Formulate a linear programming model that will enable Sunco to maximize daily profits. b) Solve the linear program using the IBM ILOG CPLEX Optimization Studio. Table 1- Gas and Crude Oil Prices for Blendi Sales Price er Barrel (s 70 60 Gas Crude Purchase Price r Barrel (S 45 35 Table 2-Octane Ratings and Sulfur Requirements for Blendin Crude Octane Rating 12 Sulfur Content (% 2.0 3.0
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