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Maximization of Profit

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AMS recently instituted an in-house recycling program. The benefits of this program include not only the benefits to the environment of recycling but also the goodwill generated by AMS's leadership in this area. The costs of recycling include all of the energy, labor, and space required to do the recycling. Suppose these benefits and costs are given by TR(Q)=100Q - 2Q2 and TC(Q) = 2Q (Note that MR = 100 - 4Q , and MC= 2 ).

a. What level of Q maximizes the profit of recycling?
b. What is marginal benefit (revenue) at this level of Q?
c. What is marginal cost at this level of Q?
d. What level of Q minimizes the total costs of recycling?
e. What level of recycling is optimal? Why?

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Solution Summary

Provides steps necessary to compute maximum profit.

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(a) Profit, P(Q) = TR(Q) - TC(Q) = 100Q - 2Q^2 - 2Q = 98Q - 2Q^2

For maximum profit, ...

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