In Exercises 29 through 35, assume that the required extreme value is a relative extremum.

A manufacturer with exclusive rights to a new industrial machine is planning to sell a limited number of them and estimates that if x machines are supplied to the domestic market and y to the foreign market, the machines will sell for 150 − x/6 thousand dollars each domestically and for 100 − y/20 thousand dollars each abroad. The operating costs are assumed to be constant.

a. How many machines should the manufacturer supply to the domestic market to generate the largest possible profit at home?

b. How many machines should the manufacturer supply to the foreign market to generate the largest possible profit abroad?

c. How many machines should the manufacturer supply to each market to generate the largest possible total profit?