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Find a maximum profit for a firm if its total revenue function is TR = 50Q...

Find a maximum profit for a firm if its total revenue function is

TR = 50Q ‒ Q2 and its total cost function is TC = 100 ‒ 4Q + 2Q2

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Answer #1

Profit=π= Total revenue- Total cost= 50Q-Q^2-(100-4Q+2Q^2)= 50Q-Q^2-100+4Q-2Q^2

π= 54Q-3Q^2-100

Differentiate profit function with respect to Q and equate it to zero.

dπ/dQ=54-6Q=0

54/6=Q

Q*=9

So profit is maximum when Q=9

Profit= 54*9-3*(9)^2-100= 486-243-100=$143

If it helps kindly upvote

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