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Question
The marginal cost function of a product is given by `"dc"/("d"x)` = 100 – 10x + 0.1x2 where x is the output. Obtain the total and the average cost function of the firm under the assumption, that its fixed cost is ₹ 500
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Solution
`"dc"/("d"x)` = 100 – 10x + 0.1x2 and k = ₹ 500
dc = (100 – 10x + 0.1 x2) dx
Integrating on both sides,
`int "dc" = int(100 - 10x + 0.1x^2) "d"x`
C = `100x - 10(x^2/2) + 0.1(x^3/3) + "k"`
Total cost C = `100x - 5x^2 + 0.1(x^3/3) + 500`
Average cost A.C = `"C"/x = (100x - 5x^2 + 0.1(x^3/3) + 500)/x`
A.C = `100 - 5x + 0.1(x^2/3) + 500/x`
A.C = `100 - 5x + x^2/30 + 500/x`
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