Maharashtra State BoardHSC Commerce 12th Board Exam
Advertisement Remove all ads

The Total Cost Function of a Firm is C = X 2 + 75 X + 1600 for Output X. Find the Output (X) for Which Average Cost is Minimum. is C a = C M at this Output? - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads

The total cost function of a firm is `C = x^2 + 75x + 1600` for output x. Find the output (x) for which average
cost is minimum. Is `C_A = C_M` at this output?

Advertisement Remove all ads

Solution

Given cost function 

`C(x) = x^2 + 75x + 1600` 

Average   `bar C (x)=(C(x))/x` 

=`(x^2+75x+1600)/x`

=`x+75+1600/x` 

Now `barC'(x)=(dbarC(x))/dx=1-1600/x^2` 

For minimum average cost `barC (x)=0` 
∴Minimum average cost=`barC(x)=40+75+1600/40=155` 

∴ `C_A=155` 

Now we find marginal cost i.e., 

`C_m=(dC)/(Dx)` 

C_m=`d/dx(x^2+75x+1600)` 

= 2x + 75               ...(1) 

∴ put x=40 in eq (1) 

`C_m=2xx40+75` 

= `80+75=155` 

`C_A=C_m  for x=40`

Concept: Maxima and Minima
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×