Question

The total cost of producing x units is Rs. (x - 4x +5) and the price is Rs. (30x) per unit. Then Maximum profit is one of the following? a 139.5 135 126
​

Answer 1

Profit P is given by

P=Revenue−Cost=Rs. {(50−  

2

x

​

)x−(  

4

x  

2

 

​

+35x+25)}=Rs.(−  

4

3

​

x  

2

+15x−25).

P=(−  

4

3

​

x  

2

+15x−25)

differentiating the above equation, we get,

dx

dP

​

=−  

2

3

​

x+15

equate  

dx

dP

​

=0

⇒−  

2

3

​

x+15=0

∴x=10

again differentiating the above equation, we get,

dx  

2

 

d  

2

P

​

=−  

2

3

​

<0 maxima

Therefore profit is maximum, when daily output is 10 items