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# maximization

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A firm uses a single with costs C=160+16Q+.1QxQ and faces the price equation P=96-.4Q.
a. Find the firmâ??s maximizing price and quantity. What is its profit?
b. Find the firmâ??s production manager claims that the firmâ??s average cost of production
is minimized at a output of 40 units. Furthermore, she that 40 units is the firmâ??s profit-
maximizing level of output.
c. Could the firm increase its profit by using a second plant (with costs identical to the first)
to produce the output in part (a)? Explain.

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https://brainmass.com/economics/output-and-costs/maximization-325661

#### Solution Preview

TC = 160 + 16Q + 0.1Q^2, P = 96 - 0.4Q

total profit = total revenue - total cost = price X quantity - TC
= (96 - 0.4Q)Q - 160 - 16Q - 0.1Q^2 = -0.5Q^2 + 80Q - 160

d(total profit)/dQ = -Q + 80 = 0 (profit maximizing condition is set the derivative to 0)

solve for Q and ...

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