Question

45. If the marginal cost function is given by M.C. = 2(2x+9)- 1/2and the fixed cost is Rs. 4, find the average cost for 8 units of output.​

Answer 1

average cost for 8 units of output is 1.

given, The marginal cost function, M.C = 2(2x + 9)^-½

we know, C = ∫(M.C) dx

= ∫2(2x + 9)^-½ dx

= 2√(2x + 9) + k , where k is constant.

here given fixed cost is Rs. 4

means if C= 4 then x = 0 and hence, 4 = 2√(2 × 0 + 9) + k

⇒4 = 2 × 3 + k ⇒k = -2

Thus total cost function is C = 2√(2x + 9) - 2

now average cost function A.C = total cost function/x

= C/x

= [2√(2x + 9) - 2]/x

for x = 8, A.C = [2√(2 × 8 + 9) - 2]/8 = 1

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