Calculus question

Question

-An office supply company sells x permanent markers per year at $p per marker. The price– demand equation for these markers is p = 10 - 0.001x. What price should the company charge for the markers to maximize revenue? What is the maximum revenue?

Answer 1

Revenue function R(x) = xp = x(10 - 0.001x) = 10x - 0.001x²;

To get critical number we have to get R'(x) and set it 0. So R'(x) = 10 - 0.002x = 0. From here x = 5000.

Becose R''(x) = - 0.002 < 0 by second derivative test we have maximum R(x) at x = 5000 markers and prise of one marker p = 10 - 0.001· 5000 = $5 and maximum revenye R_max= R(5000) = $25000