# Answer to Question #59842 in Microeconomics for Mike

Question #59842

Maximizing profits from cost function of C=50 + 4Q^2 with price of $40

Expert's answer

Let P(q) be the profit function,

P (q) =q*p (q)-C (q) =q*40-(50+4q^2) =-4q^2+40q-50

To maximize the profit function, take its first derivative and set equal to zero.

dP/dq=0

dP/dq (-4q^2+40q-50)=0

-8*q+40=0

q=5

The maximum profit is P (5) .

P (q) =q*p (q)-C (q) =q*40-(50+4q^2) =-4q^2+40q-50

To maximize the profit function, take its first derivative and set equal to zero.

dP/dq=0

dP/dq (-4q^2+40q-50)=0

-8*q+40=0

q=5

The maximum profit is P (5) .

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