If the total revenue function for a computer is R(x) = 1600x − 26x2 − x3, find the level of sales, x, that maximizes revenue and find the maximum revenue in dollars.

Question

x = _____ computers ?

R(x) = $ ______ ?

Answer 1

1600x -26x^2 -x^3

take the derivative and set equal to zero

1600-52x -3x^2 = 0

3x^2 +52x -1600 = 0 use the quadratic formula

x = -52/6 + (1/6)sqr(52^2 + 12(1600)) = (-52+148)/6 = 96/6= 16 (ignore the negative square root)

x= 16 computers

plug 16 into the revenue equation

maximum revenue = 1600(16) - 26(16)^2 - (16)^3 = 25,600 - 6,656 -4,096 = $14,848