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1.     Given a firm’s demand function, P = 24 - 0.5Q and the average cost function, AC = Q2 – 8Q + 36  + 3/Q, calculate the level of output Q which  a)  maximizes total revenue
b) maximizes profits
```
7 years ago

## Answers : (1)

30 Points
```										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)
Please feel  free to post as many doubts on our discussion forum as you can. If you  find any questionDifficult to understand - post it here  and we will get you the answer and detailed solution very quickly. Weare all  IITians and here to help you in your IIT JEE preparation.All the best  Sanjay!!!Regards,Askiitians  ExpertsPriyansh Bajaj?
```
7 years ago
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