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Dinoco produces three types of oil products: domestic oil, petrol for car and aviation fuel. Each product must meet the minimum average octane regulation. The average octane levels must be at least 5 for domestic oil, 10 for petrol and 8 for aviation fuel. To produce these products, Dinoco purchases two types of crude oil; Arabian Night (at $120 per barrel) and Brent (at $90 per barrel). Each day, at most 8,000 barrels of each type of crude oil can be purchased. Crude Oils must be distilled to be used for the production of Dinoco's three products. Each day, at most 12,000 barrels of crude oil can be distilled. It costs $20 to distil a barrel of oil (whether it is Brent or Arabian Night). The results of distillation are as follows: • Each barrel of Arabian Night yields 0.6 barrels of naphtha, 0.3 barrel of distilled 1, and 0.1 barrel of distilled 2. Each barrel of Brent yields 0.4 barrels of naphtha, 0.4 barrel of distilled 1, and 0.2 barrel of distilled 2. Dinoco's three products are produced by mixing naphtha, distilled 1, and distilled 2. Due to the regulation, however, distilled naphtha cannot be used for aviation oil. The octane level for types of distilled are 12, 10, and 4 for naphtha, distilled 1 and distilled 2, respectively. All domestic oil produced can be sold at $200 per barrel; all petrol produced sold at $300 per barrel, and all aviation fuel sold at $280 per barrel. For company's product mix consideration, at least 2,500 barrels of each product must be produced daily. (a) Formulate an LP to maximise Dinoco's daily profit. You must list any assumption(s) you have made in your formulation. And, use Management Scientist to find the optimal solution.