Answer to Question #259050 in Calculus for Anice

Question

Find the number of units that must be produced and sold in order to yield the maximum profit, given the following equations for revenue and cost:

R(x) = 30x - 0.5x 2

C(x) = 5x + 7.

A. 32 units

B. 26 units

C. 35 units

D. 25 units

Answer 1

$\displaystyle \text{The profit is given by }\\ p(x) = R(x)-C(x)\\ = 30x - 0.5x^2-5x-7\\ = -0.5x^2+25x-7\\ p'(x) = -x+25\\ \text{When profit is maximum, $p'(x) = 0$ }\\ \therefore x = 25$