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The marginal cost function of a product is given by dcddcdx = 100 – 10x + 0.1x2 where x is the output. Obtain the total and the average cost function of the firm under the - Business Mathematics and Statistics

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प्रश्न

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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उत्तर

`"dc"/("d"x)` = 100 – 10x + 0.1xand 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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Application of Integration in Economics and Commerce
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अध्याय 3: Integral Calculus – 2 - Exercise 3.2 [पृष्ठ ७२]

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सामाचीर कलवी Business Mathematics and Statistics [English] Class 12 TN Board
अध्याय 3 Integral Calculus – 2
Exercise 3.2 | Q 6 | पृष्ठ ७२

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