Priyansh Bajaj AskiitiansExpert-IITD
Last Activity: 14 Years ago
Dear Sanjay,
Solution:- (a) Total Revenue (TR) = P*Q = (24 - 0.5Q) * Q
To find the max value of Total Revenue, differentiate it and equate it to zero.
d(TR)/dQ = 0 or d(24Q - 0.5Q2)/dQ = 0
24 - Q = 0 or Q = 24 (ANS)
(b) Total cost (TC) = (AC) * Q = (Q2 - 8Q +36 +3/Q) * Q = (Q3 - 8Q2 +36Q +3)
Profit (P) = [TR - TC] = [(24Q - 0.5Q2) - (Q3 - 8Q2 +36Q +3)] = (-12Q +7.5Q2 -Q3 -3)
To find the max value of Profit, differentiate it and equate it to zero.
d(P)/dQ = 0 or d(-12Q +7.5Q2 -Q3 -3)/dQ = 0
-12 +15Q -3Q2 = 0 or Q2- 5Q+4 =0
Q =1 or 4
At Q =1, P = - 8.5 and at Q = 4, P = 5
So, 'P' is maximum at Q =4 (ANS)
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All the best Sanjay!!!
Regards,
Askiitians Experts
Priyansh Bajaj
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