Question

Suppose a baby food company has determined that its total revenue R for its food is given by R = − x ^3 + 102 x ^2 + 1575 x where R is measured in dollars and x is the number of units (in thousands) produced. What production level will yield a maximum revenue?

Answer 1

75 thousand

Explanation:

R = -x³ + 102x² + 1575x

To maximize R, find dR/dx and set to 0:

dR/dx = -3x² + 204x + 1575

0 = -3x² + 204x + 1575

0 = x² − 68x − 525

0 = (x + 7) (x − 75)

x = -7 or 75

Since x can't be negative, x = 75.

Therefore, the revenue is a maximum when 75 thousand units are produced.