A firm wants to maximize its profit. The total cost function is C = 370Q + 550 and revenue is R = 730Q-3Q^{2}. Find the output for which profit is maximum and also find the profit amount at this output.

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#### 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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