Problem 1. [30 points] Consider a firm with a plant in the U.S. and the U.K.. A U.S.based shipper charges \$1.10 per unit to ship between the two countrics. Assume no taxes and consider the following data: (a) Suppose that the exchange rate is 21.00=$1.32. What is the best production and distribution plan, i.e., how much should be made in each country, and how much should be shipped between countries? (b) Given your plan in part a, what is the profit in each country (expressed in dollars)? Problem 2. [20 points] The three-station work cell is illustrated below. It has two machines at station 1 in parallel (i.e., the product needs to go through only one of the two machines before proceeding to station 2 ). (a) What is the throughput time of this work cell? (b) What is the bottleneck station? (c) What is the bottleneck time of this work cell? (d) If the firm operates 8 hours per day, 6 days per week, what is the weekly capacity of this work cell? Show your work