# Math Help - Need help

1. ## Need help

A manufacturuer can produce radios at a cost of $5 apiece. The radios have been selling for$9 apiece, and at this price, consumers have been buying 6,000 radios a month. The manufacturer is planning to raise the price of radios and estimates that for each \$1 increase in price, 300 fewer radios will be sold a month. What should be the selling price in order to maximize profit?

Need step by step help solving this problem.

2. Here are some steps you could try.

1. Find the function relating price to quantity sold.
ie. f(price)=quantity

2. Find the functions for gross profit and costs in terms of the above function.
ie. f(price)=gross and f(price)=costs

3. Subtract to get the net profit function.
ie. f(price)=net

4. Differentiate to find the maximum