A company estimates that the price (in dollars) needed to sell cell-phone accessories…
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
A company estimates that the price p (in dollars) needed to sell q cell-phone accessories is given by p(q)=120−0.5q for 0≤q≤240. The total cost of producing q accessories is C(q)=40q+5,000 dollars.
(a) Express the total revenue R(q) and the total profit P(q) as explicit functions of q. Do not simplify the expressions yet.
(b) Determine the production level q that maximizes profit. Then find the corresponding selling price.
(c) Calculate the maximum profit the company can earn.
(d) Verify that the production level found in part (b) indeed yields a maximum, and not a minimum, for the profit function. State the justification clearly.