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?

The production level will yield a maximum revenue when production level is approximately equal to 75,000.

Step-by-step explanation:

Revenue is given by  

R(x) =

First, we differentiate R(x) with respect to x, to get,

Equating the first derivative to zero, we get,

Solving, with the help of quadratic formula, we get,

Again differentiation R(x), with respect to x, we get,

At x = 75

Thus, maxima occurs at x = 75 for R(x).

Thus, the production level will yield a maximum revenue when production level is approximately equal to 75,000.

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step-by-step explanation: