Peridatt Audio manufactures specialist sound amplifiers. The company have identified the following expressions to represent the demand for their products and the total cost of their operations:
where x is the number of amplifiers produced and sold. (Production is to order only.)
(a) Determine the profit equation for the company.
(b) Use the profit equation to find the profit maximizing level of output and price, and the optimum profit.
(c) Find the second derivative of the profit equation and use it to confirm that the output level in (b) does occur at a maximum.