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    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)

    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


    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.