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Problem 2 [30 points]: An oil company produces three brands of oils: Regular, Multigrade, and Supreme. Each brand of oil is composed of one or more of four crude stocks, each having a different viscosity index. The relevant data concerning the crude stocks are: Crude Stock 1 Viscosity Index 20 2 40 Cost ($/barrel) 7.10 8.50 7.70 9.00 Supply Per Day (barrels) 1,000 1,100 1,200 1,100 3 30 55 4 Each brand of oil must meet a minimum standard for viscosity index, and each brand sells at a different price. The relevant data concerning the three brands of oil are: Brand Minimum Selling price Daily Maximum Sales Viscosity Index ($/barrel) (barrels) Regular 25 8.50 2,000 Multigrade 30 9.00 1,500 Supreme 50 10.00 800 a) Define the decision variables and write down the detailed mathematical formulation of the oil company's problem to maximize its total profit for a single day. [15 points] b) Solve the optimization problem by Excel Solver. Write down the company's optimal production plan and optimal total profit. [15 points]
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