BS Oil 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 differs in composition and therefore contains different chemical mixes. Each barrel of Country A’s crude oil yields 0.3barrel of kerosene, 0.4 barrels of asphalt base, 0.2 barrels of petroleum naphtha, and 0.1 barrels of waste. On the other hand, each barrel of Country B’s crude oil yields 0.4 barrels of kerosene,0.2 barrels of asphalt base, 0.3 barrels of petroleum naphtha, and 0.1 barrels of waste. The crude oils also differ in cost and availability. BS Oil 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. BS Oil 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. •Formulate this problem algebraically, how can these requirements be met to minimize cost?
BS Oil 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 differs in composition and therefore contains different chemical mixes. Each barrel of Country A’s crude oil yields 0.3barrel of kerosene, 0.4 barrels of asphalt base, 0.2 barrels of petroleum naphtha, and 0.1 barrels of waste. On the other hand, each barrel of Country B’s crude oil yields 0.4 barrels of kerosene,0.2 barrels of asphalt base, 0.3 barrels of petroleum naphtha, and 0.1 barrels of waste. The crude oils also differ in cost and availability. BS Oil 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. BS Oil 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.
•Formulate this problem algebraically, how can these requirements be met to minimize cost?
| Country A | Country B | |
| Cost | 20 | 15 |
| Barrel available per day | 9000 | 6000 |
| Content Per barrel | ||
| Country A | Country B | |
| Kerosene | 0.3 | 0.4 |
| Asphalt base | 0.4 | 0.2 |
| Petroleum naptha | 0.2 | 0.3 |
| Waste | 0.1 | 0.1 |
| Demand in barrels | ||
| Kerosene | 2000 | |
| Asphalt base | 1500 | |
| Petroleum naptha | 500 | |
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