Business: Maximizing Profit An electronics store can sell 35 cell phones per week at a price of $200. The manager estimates that for each $20 price reduction she can sell 9 more per week. The phones cost the store $100 each, and fixed costs are $700 per week.
a. If x is the number of $20 price reductions, find the price p(x) and enter it in y1. Then enter the quantity function q(x) in y2.
b. Make y3 the revenue function by defining y3 = y1 y2 (price times quantity).
c. Make y4 the cost function by defining y4 as unit cost times y2 plus fixed costs. d. Make y5 the profit function by defining y5 = y3 - y4 (revenue minus cost).
e. Turn off y1, y2, y3, and y4 and graph the profit function y5 for x-values [-10, 10], using TABLE or TRACE to find an appropriate y-interval. Then use MAXIMUM to maximize it.
f. Use CALCULATE to find the price and the quantity for this maximum profit.
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