A store can sell 12 telephone answering machines per day at a price of $200 each. The manager estimates that for each $10 price reduction she can sell 2 more per day. The answering machines cost the store $80 each.
Find the price and the quantity sold per day to maximize the company’s profit.
Hint: Let x be the number of 10- dollar price reductions. Find in this order the following functions:
n(x) = number of items sold,
the price function p(x),
the cost function C(x),
the revenue function R(x),
and the profit function P(x).
Then maximize the profit function.