Chapter 7.3, Problem 43E

Maximizing profit. A store sells two brands of camping chairs. The store pays $60 for each brand A chair and $80 for each brand B chair. The research department has estimated the weekly demand equations for these two competitive products to be

     $\begin{array}{ll}x=260-3p+q\hfill & \text{Demand equation for brand}A\hfill \\ y=180+p-2q\hfill & \text{Demand equation for brand}B\hfill \end{array}$

where p is the selling price for brand A and q is the selling price for brand B.

1. (A) Determine the demands x and y when p = $100 and q = $120; when p = $110 and q = $110.
2. (B) How should the store price each chair to maximize weekly profits? What is the maximum weekly profit? [Hint: C = 60x + 80y, R = px + qy, and P = R − C.]