Company XYZ manufactures three products A, B, and C. The production of these products requires three basic resources Labor, Steel, and, Copper: Resources Labor Steel Copper Market Price ($) Variable Cells A 1 3 2 4 Cell $B$2 Number of Product A: $B$3 Number of Product B: $B$4 Number of Product C: Product B Name 2 1 3 5 For example, one unit of product A requires 1 unit of labor, 3 units of Steel, and 2 units of Copper. The available quantities of the resources are given in the last column, and the last row presents the per unit market price of the three products. C 4 1 0 3 2 Because of marketing considerations, the manager of the company wants the fraction of units of product C produced to be at least 40% of the total number of units produced of the three products. According to historical data, buyers of B use their credit card to pay while the buyers of A and C prefer to pay cash. For this reason, the manager wants that the revenue ($) made from the sales of product B to be no more than the amount collected from the sales of A and C together. The following table is from the sensitivity report given by the Excel Solver. Based on this table, answer the following questions: Quantity Available 120 90 70 Final Reduced Value Cost 20 10 20 0 0 0 Objective Allowable Allowable Coefficient Increase Decrease 4 5 0.636363636 2.909090909 3 9.4 0.5 6.4 3.5 (a) Formulate a Linear Programming (LP) Problem that can help the manager find the best production strategy [5 pts]. (b) What is the optimal production plan [5 pts]? (c) If the market price of Product B drops to $2 per unit, will the current production plan still be optimal? Why or why not [10 pts]? (d) If the market price of Product A changes from the current price to $7 per unit, how much additional revenue can the company earn [10 pts]?

Company XYZ manufactures three products A, B, and C. The production of these products requires three basic resources Labor, Steel, and, Copper: For example, one unit of product A requires 1 unit of labor, 3 units of Steel, and 2 units of Copper. The available quantities of the resources are given in the last column, and the last row presents the per unit market price of the three products. 2 Because of marketing considerations, the manager of the company wants the fraction of units of product C produced to be at least 40% of the total number of units produced of the three products. According to historical data, buyers of B use their credit card to pay while the buyers of A and C prefer to pay cash. For this reason, the manager wants that the revenue (\$) made from the sales of product B to be no more than the amount collected from the sales of A and C together. The following table is from the sensitivity report given by the Excel Solver. Based on this table, answer the following questions: (a) Formulate a Linear Programming (LP) Problem that can help the manager find the best production strategy [5 pts]. (b) What is the optimal production plan [5 pts]? (c) If the market price of Product B drops to \$2 per unit, will the current production plan still be optimal? Why or why not [10pts] ? (d) If the market price of Product A changes from the current price to $7 per unit, how much additional revenue can the company earn [10 pts]