123 Oil Company manages a refinery in the Gulf of Mexico. The refinery distills crude oil from two sources, Country A and Country B, into three main products: kerosene, asphalt base, and petroleum naphtha. The two Countries oil differ in composition and therefore contains different chemical mixes. Each barrel of Country A’s crude oil yields 0.3 barrel of kerosene, 0.4 barrel of asphalt base, 0.2 barrel of petroleum naphtha, and 0.1 barrel of waste. On the other hand, each barrel of Country B’s crude oil yields 0.4 barrel of kerosene, 0.2 barrel of asphalt base, 0.3 barrel of petroleum naphtha, and 0.1 barrel of waste. The crude oils also differ in cost and availability. JROC can purchase up to 9000 barrels per day from Country A at $20 per barrel. Up to 6000 barrels per day of Country B are also available at the lower cost of $15 per barrel because of shorter transportation costs. JROC’s contracts with independent distributors require it to produce at least 2000 barrels per day of kerosene, at least 1500 barrels per day of asphalt base, and at least 500 barrels per day of petroleum naphtha. How can these requirements be met to minimize cost? • Formulate this problem algebraically. • Solve this problem in Excel.
123 Oil Company manages a refinery in the Gulf of Mexico. The refinery distills crude oil from two sources, Country A and Country B, into three main products: kerosene, asphalt base, and petroleum naphtha. The two Countries oil differ in composition and therefore contains different chemical mixes. Each barrel of Country A’s crude oil yields 0.3 barrel of kerosene, 0.4 barrel of asphalt base, 0.2 barrel of petroleum naphtha, and 0.1 barrel of waste. On the other hand, each barrel of Country B’s crude oil yields 0.4 barrel of kerosene, 0.2 barrel of asphalt base, 0.3 barrel of petroleum naphtha, and 0.1 barrel of waste. The crude oils also differ in cost and availability. JROC can purchase up to 9000 barrels per day from Country A at $20 per barrel. Up to 6000 barrels per day of Country B are also available at the lower cost of $15 per barrel because of shorter transportation costs. JROC’s contracts with independent distributors require it to produce at least 2000 barrels per day of kerosene, at least 1500 barrels per day of asphalt base, and at least 500 barrels per day of petroleum naphtha.
How can these requirements be met to minimize cost?
• Formulate this problem algebraically.
• Solve this problem in Excel.
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