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 wher
e R is measured in dollars and x is the number of units (in thousands) produced. What production level will yield a maximum revenue?
1 answer:
Answer:
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.
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