Price Per Unit Question

Question

Supposed that the price per unit in dollars of a cell phone production is modeled by p=55-0.0125x, where x Is in thousands of phones produced, and the revenue is represented by thousands of dollars is R=x*p. Find the production level that will maximize revenue

Answer 1

P= 55 - 0.0125x

R = xP = 55x - 0.0125x^2

take the derivative and set equal to zero, then solve for x = the revenue maximizing output level

R' = 55- 0.025x = 0

x = 55/.025 = 2,200 thousand phones = 2 million 2 hundred thousand phones is the production level that will maximize revenue

max R = 55(2200) - 0.0125(2200)^2 = 121,000 - 60,500 = 60,500 x 10^3 = 60 million, 500 thousand dollars.