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kolbaska11 [484]
3 years ago
15

Suppose a baby food company has determined that its total revenue R for its food is given by R = − x 3 + 39 x 2 + 945 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?
Mathematics
1 answer:
Paraphin [41]3 years ago
4 0

Answer:

35,000 units

Step-by-step explanation:

Total revenue is:

R = -x^3+39x^2+945x

The maximum revenue is attained at the production level for which the derivate of the revenue function is zero:

R = -x^3+39x^2+945x\\R'=0=-3x^2+78x+945\\x=\frac{-b\pm\sqrt{78^2-(4*(-3)*945)} }{-6}\\x_1=35\\x_2=-9

Since production cannot be negative, revenue will be at a maximum when x = 35, or when the production level is 35,000 units.

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