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10 October, 15:03

Suppose a baby food company has determined that its total revenue R for its food is given by R = - x 3 + 33 x 2 + 720 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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  1. 10 October, 16:26
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    A production level of 30 thousand units (x = 30)

    Step-by-step explanation:

    To find the production level (value of x) that will yield the maximum revenue, we can take the derivative of the function R in relation to x and find when it is equal to 0:

    dR/dx = - 3x2 + 66x + 720 = 0

    x2 - 22x - 240 = 0

    Solving the quadratic equation using Bhaskara's formula, we have:

    Delta = (-22) ^2 + 4*240 = 1444

    sqrt (Delta) = 38

    x1 = (22 + 38) / 2 = 30

    x2 = (22 - 38) / 2 = - 8

    The negative value is not valid for our problem, so we have that the value that gives the maximum revenue is x = 30
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