A monopolist sells Product A and Product B. A unit of Product A costs 5 dollars to procure while a unit for Product B costs 10 dollars to procure. Let PA be the selling price of Product A and PB be the selling price of Product B. And, let QA be the demand for Product A and QB be the demand for Product B. The two demands interact so that

QA=100 - 20PB - PA, and

QB=200 - 10PA - PB.

1) Write an expression for profit as a function of PA and PB?

This questions belongs in the Business / Economics section:

Profit (p) = Revenue (R) - Costs (C)

Revenue (R) = Price (P) x Quantity (Q)

Given that Cost of A = $5 and Cost of B = $10, let PA and PB represent prices, respectively.

Profit (p) = (PAQA + PBQB ) - (5QA + 10QB )

Looking at the entire left side of the equal sign, the first bracket is the revenue, and the 2nd is the cost.

2) What are the prices of PA and PB that maximize profits?

3) How much is sold of each product at these prices?