If a manufacturer sells an article for p dollars, he finds that n = (125 − p) articles can be sold per week. The cost of producing n articles is c = 100 + 100n − ((n^2)/2) dollars.
a. Find the price (p) that maximizes his profits.
b. Use and document Excel to simulate the problem and evaluate the price (p) that maximizes his profits, as well as the total cost and total revenues associated.