Chapter 7.3, Problem 44E

Maximizing profit. A store sells two brands of laptop sleeves. The store pays $25 for each brand A sleeve and $30 for each brand B sleeve. A consulting firm has estimated the daily demand equations for these two competitive products to be

     $\begin{array}{ll}x=130-4p+q\hfill & \text{Demand equation for brand}A\hfill \\ y=115+2p-3q\hfill & \text{Demand equation for brand}B\hfill \end{array}$

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 = $40 and q = $50; when p = $45 and q = $55.
2. (B) How should the store price each brand of sleeve to maximize daily profits? What is the maximum daily profit? [Hint: C = 25x + 30y, R = px + qy, and P = R − C.]