Answer to Question #59842 in Microeconomics for Mike

Question

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

Answer 1

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) .