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The marginal cost of production of a firm is given by C'(x) = 5 + 0.13x, the marginal revenue is given by R'(x) = 18 and the fixed cost is ₹ 120. Find the profit function

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प्रश्न

The marginal cost of production of a firm is given by C'(x) = 5 + 0.13x, the marginal revenue is given by R'(x) = 18 and the fixed cost is ₹ 120. Find the profit function

योग
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उत्तर

MC = C'(x) = 5 + 0.13x

C(x) = `int "C'"(x)  "d"x + "k"_1`

= `int (5 + 0.13x)  "d"x + "k"_1`

= `5x + 0.13/2 x^2 + "k"_1`

When quantity produced is zero, fixed cost is 120

i.e When x = 0, C = 120

⇒ k1 = 120

Cost function is 5x + 0.065x2 + 120

Now given MR = R'(x) = 18

R(x) = `int 18  "d"x + "k"_2`

= `18x + "k"_2`

When x = 0

R = 0

⇒ k2 = 0

Revenue = 18x

Profit P = Total Revenue – Total cost

= 18x – (5x + 0.065x2 + 120)

Profit function = 13x – 0.065x2 – 120

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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 14 | पृष्ठ ७२

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