Gladeet Domestic offers busy professionals a clothes-ironing service. The equations that represent the connections between their volume of business in thousands of clients (x), and firstly the price they charge, and secondly the total cost they incur are:
(a) Derive the profit equation for their business.
(b) What are the profit maximizing levels of output and price, and the maximum profit they can obtain?
(c) Obtain the second derivative of the profit equation and use it to prove that the output level in (b) occurs at a maximum