In the exchange rate model in Example 7.2, suppose the company continues to manufacture its product in the United States, but now it sells its product in the United States, the United Kingdom, and possibly other countries. The company can independently set its price in each country where it sells. For example, the price could be $150 in the United States and £110 in the United Kingdom. You can assume that the demand function in each country is of the constant elasticity form, each with its own parameters. The question is whether the company can use Solver independently in each country to find the optimal price in this country. (You should be able to answer this question without actually running any Solver model(s), but you might want to experiment, just to verify your reasoning.)
EXAMPLE 7.2 PRICING WITH EXCHANGE RATE CONSIDERATIONS AT MADISON
We continue Example 7.1 but now assume that Madison manufactures its product in the United States and sells it in the United Kingdom (UK). Given the prevailing exchange rate in dollars per pound, Madison wants to determine the price in pounds it should charge in the UK so that its profit in dollars is maximized. The company also wants to see how the optimal price and the optimal profit depend on exchange rate fluctuations.
Objective To use a nonlinear model to find the price in pounds that maximizes the profit in dollars.
WHERE DO THE NUMBERS COME FROM?
The only new input in this model is the exchange rate, which is readily available. For example, you can find exchange rates at http://www.oanda.com/convert/classic.