An industrial firm makes two products, A and B. These products require water resources where they are very scarce. 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 the 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 (16 - A) and for product B is (18-2.5B). Suppose the total amount of A and B could not exceed the total amount of Tmax. Where Tmax = 10. Please use "Lagrange Multiplier" method to determine what are the amounts of A and B, and their unit prices, that maximize total revenue (Set the marginal increments at 1).
An industrial firm makes two products, A and B. These products require water resources where they are very scarce. 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 the 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 (16 - A) and for product B is (18-2.5B). Suppose the total amount of A and B could not exceed the total amount of Tmax. Where Tmax = 10. Please use "Lagrange Multiplier" method to determine what are the amounts of A and B, and their unit prices, that maximize total revenue (Set the marginal increments at 1).
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