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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.
Profit = -1500 + 205PA - 30PAPB + 310PB - PB2 - PA2
a) What are the prices of PA and PB that maximize profits?b) How much is sold of each product at these prices?
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