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Sunco Oil manufactures three types of gasoline (gas 1, 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 below. Sunco can purchase up to 5000 barrels of eachtype of crude oil daily. The three types of gasoline differ in their octane rating and sulfur content. The crude oil blended to form gas 1 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 below. It costs $4 to transform one barrel of oil into one barrel of gasoline, and Sunco's renery can produce up to 14,000 barrels of gasoline daily. Sunco's customers require the following amounts of each gasoline: 3000 barrels of gas 1 per day, 2000 barrels of gas 2 per day, and 1000 barrels of gas 3 per day. The company considers it an obligation to meet those demands. Formulate a linear programming model that will enable Sunco to maximize its daily prots (profits = revenues - costs). Crude oil blending was one of the earliest successful large-scale applications of linear pro- gramming in an industrial setting.
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