Question

1. A firm has a revenue fenetion R= 8D, where
R is the gross revence and is quantity sold.
The production cost is given by C= 150000+60.
(D/900) find the total profit function and
the number of units sold to get maximum profit
​

Answer 1

Given :  A firm has a revenue function R= 8D, where  R is the gross revence and D is quantity sold.  The production cost is given by C=  50000+60.(D/900)²

To find :  total profit function and  the number of units sold to get maximum profit

Solution:

R = 8D

C = 150000  + 60 (D/900)²

Profit = Revenue - Cost

=> P = R - C

=> P = 8D  -  150000  - 60 (D/900)²

dP/dD  = 8  -  120D/900²

dP/dD  =  0

=> 8  -  120D/900²  = 0

=> D = 8 * 900²/120

=> D = 54000

d²P/dD²  = -240D/900²   = - 16  <  0   for  D  = 54000

Hence Profit is maximum when D = 54000

total profit function  = 8D  -  150000  - 60 (D/900)²

54000 number of units sold to get maximum profit

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