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प्रश्न
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.
उत्तर
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
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