HSC Commerce (Marketing and Salesmanship) 12th Board ExamMaharashtra State Board
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# 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? - HSC Commerce (Marketing and Salesmanship) 12th Board Exam - Mathematics and Statistics

#### Question

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?

#### 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

Is there an error in this question or solution?

#### APPEARS IN

2017-2018 (March) (with solutions)
Question 3.2.2 | 4.00 marks
Solution 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? Concept: Maxima and Minima.
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