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QopyQat Printing: Profit Maximization

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QopyQat specializes in printing business cards and resumes, using the latest laser technology. After analysis of the business, the manager has decided that weekly demand can be approximated by

Q = 25,000 - 100P

The firm's cost function is

C = 25,000 + 13Q + 0.002Q^2 (Q square)

where Q is output per week.

a) Determine the firm's optimal output and price
b) The night supervisor believes that keeping QopyQat open for two more hours in the evening would substantially increase volume. The manager is willing to stay open for two hours over the next three months as an experiment. What results would lead you to recommend that the store remain open later in the evening on a permanent basis?
c) A former employee decides to sue QopyQat, alleging employment discrimination. Although management claims innocence, they agree to settle out of court. The settlement requires QopyQat to pay the employee $10,000 per month for the next year. Determine the optimal price and output for the shop under these new conditions.

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Solution Preview

a) The firm maximizes its profit when Marginal Revenue (MR) = Marginal Cost (MC).

Q = 25000 - 100P
100P = 25000 - Q
P = 250 - 0.01Q

To find MR, first find Total Revenue (TR):
TR = (250 - 0.01Q)Q
TR = 250Q - 0.01Q^2

MR is the ...

Solution Summary

Given QopyQat's Demand and Cost functions, this solution shows how to calculate the firm's optimal price and output, even when conditions change.