#### Question

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.

clickto share

#### 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

Is there an error in this question or solution?

#### APPEARS IN

Solution for question: 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. concept: null - Maxima and Minima. For the courses HSC Commerce, HSC Commerce (Marketing and Salesmanship)