# A firm wants to maximize its profit. The total cost function is C = 370Q + 550 and revenue is R = 730Q-3Q2. Find the output for which profit is maximum and also find the profit amount at this output. - Mathematics and Statistics

A firm wants to maximize its profit. The total cost function is C = 370Q + 550 and revenue is R = 730Q-3Q2. Find the output for which profit is maximum and also find the profit amount at this output.

#### Solution

Profit function P=R-C

P=(730Q-3Q^2)-(370Q+550)

=360Q-3Q^2-550

"dP"/"dQ"=360-6Q

(d^2P)/(dQ^2)=-6

for maxima or minima "dP"/"dQ"=0

360-6Q=0

6Q=360

Q=60

((d^2P)/(dQ^2))_(Q=60)=-6<0

We get maximum at Q=60

P_(max)=360xx60-3xx60^2-550

=21600-10800-550

=10250

Concept: Maxima and Minima
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