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?

Question

Madison

Mathematics

2 January, 14:41

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?

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Answers (1)

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Leanna Thornton · Answer 1

75 thousand

Step-by-step 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.