Continuing Problem 6, suppose the company is selling in the United States, the United Kingdom, and Japan. Assume the unit production cost is $50, and the exchange rates are 1.52 ($/£) and 0.01157 ($/¥). Each country has its own constant elasticity demand function. The parameters for the United States are 19,200,000 and -2; the parameters for the United Kingdom are 10,933,620 and -2.2; and the parameters for Japan are 15,003,380,400 and -1.9. The company has a production capacity of 3000. Therefore, the company can sell only as many units, in total, to all three countries as it can produce.
a. Develop a spreadsheet model that determines the prices the company should charge and the numbers of units it should sell in each of the three countries to maximize its total profit in dollars. (Note that if total demand is greater than capacity, the company has to decide how much to sell in each country. Therefore, the amounts to sell become changing cells.)
b. When the capacity is 3000, is all of this capacity used? Answer the same question if the capacity is increased to 4000.
c. Discuss the customer behavior that might result from the solution to the model in part a. If the company sets its price in one country relatively low compared to its price in another country, what might customers do?