# Evaluating Profit

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Acme estimates marginal revenue on a product to be 200q^-1/3 dollars per unit when the level of production is q units. The corresponding marginal cost is 2q dollars per unit. Suppose the profit is $300 when the level of production is 1 unit. What is Acme's profit when 8 units are produced?

(Note: P'(t) = R'(t) - C'(t) and P(0) = 0)

$937

$987

$1037

$1087

$1137

$1187

$1237

none of these

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#### Solution Preview

Given R'(q)=200*q^(-1/3) and C'(q)=2q. Note that P'(q) = R'(q) - C'(q). So,

P(q)= 200*q^(-1/3) - 2q

So, integrating it, we have

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#### Solution Summary

Profit is evaluated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

$2.49