Problem 1 (15 marks) Consider an auto parts firm with plants for brake shoes in the U.S., Canada, and Mexico. The firm has a total weekly output of 14,000 units. All output is shipped to a distribution center in Kansas, and shipping costs from the three plants to the center are equal. There are no Canadian and Mexican domestic sales. All sales are in the U.S. market distributed from the Kansas center. The plants have the marginal costs given in the table below. a) What is the optimal allocation of the total output of 14,000 units per week among the three plants? Briefly explain your reasoning. (Note: No complicated calculations are required. The allocation of output should be such that at the margin, the costs in each plant are approximately the same). b) If the firm was only producing 3000 units, and it was doing so optimally, and it got an order for an additional 1000 units, where would that incremental 1000 be produced? c) If the firm was forced to close a plant and still needed to produce 14,000 units, what plant should it close and how should it allocate production across the other plants? Units Marginal Cost ($ per unit) Produced U.S. Canada Mexico 0 1.000 6.40 5.40 6.00 2,000 6.20 6.50 5.14 3.000 6.24 5.69 5.29 4,000 6.30 6.8 6.46 5.000 6.50 7.10 6.70 6,000 6.71 7.32 7.00 7,000 7.00 7.55 7.40 8.000 7.35 7.79 7.90 The table can be read as follows; the first 1000 units produced in the U.S. will be manufactured at a cost of $6.40 per unit; the next 1000 units produced in the U.S. will be manufactured at a cost of $6.20 per unit, etc