Question

A company employed a cost accountant who developed two functions to describe the operation of a firm.He found out that the marginal revenue function was governed by MR=25-5x-2x^2 and MC=15-2x-x^2. Determine the profit maximizing output and the total profit at that point

Answer 1

$$25-5x-2x^2=15-2x-x^2$$

$$MR=MC$$

$$x=2$$

$$TR=\int MR=25x-5\frac{x^2}{2}-2\frac{x^3}{3}$$

$$TC=\int MC=15x-x^2-\frac{x^3}{3}$$

$$\pi=TR-TC=10x-1.5x^2-\frac{1}{3}x^3=11\frac{1}{3}$$