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$