1. An industrial firm makes two products, A and B. These products require water and other resources. Water is the scarce resourcethey have plenty of other needed resources. The products they make are unique, and hence they can set the unit price of each product at any value they want to. However experience tells them that the higher the unit price for a product, the less amount of that product they will sell. The relationship between unit price and quantity that can be sold is given by the following two demand functions. Assume for simplicity that the unit price for product A is (8 A) and for product B is (6 1.5B).

b. Suppose the total amount of A and B could not exceed some amount Tmax.

Use Lagrange Multiplier method to determine what are the amounts of A and B, and their unit prices, that maximize total revenue, if (i) Tmax = 10