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If the marginal cost (MC) of production of the company is directly proportional to the number of units (x) produced, then find the total cost function, when the fixed cost is ₹ 5,000

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प्रश्न

If the marginal cost (MC) of production of the company is directly proportional to the number of units (x) produced, then find the total cost function, when the fixed cost is ₹ 5,000 and the cost of producing 50 units is ₹ 5,625

बेरीज
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उत्तर

M.C αx

M.C = λx

fixed cost k = ₹ 5000

Cost function C = `int ("M.C")  "d"x`

= `int lambdax  "d"x`

C = `(lambdax^2)/2 + "k"`

⇒ C = `lambda (x^2/2) + 5000`  ........(1)

When x = 50 then C = 5625

5625 = `(lambda(50)^2)/2 + 5000`

5625 – 5000 = `(lambda(2500))/2 = 1250 lambda`

`1250 lambda = 625`

⇒ `lambda = 625/1250 = 1/2`

∴ Required total cost function from equation (1)

C = `1/2(x^2/2) + 5000`

∴ C = `x^2/4 + 5000`

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Application of Integration in Economics and Commerce
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पाठ 3: Integral Calculus – 2 - Exercise 3.2 [पृष्ठ ७३]

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सामाचीर कलवी Business Mathematics and Statistics [English] Class 12 TN Board
पाठ 3 Integral Calculus – 2
Exercise 3.2 | Q 18 | पृष्ठ ७३

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