If C ( x ) = x 3 - 24 x 2 + 600 x , calculate the range where A C falls.

Given, C ( x ) = x 3 - 24 x 2 + 600 x Average cost A C = Total cost Number of units A C = x 3 - 24 x 2 + 600 x x = x 2 - 24 x + 600 To check range of A C , differentiate it and equate to zero. d d x ( x 2 - 24 x + 600 ) = 0 2 x - 24 = 0 x = 12 Hence, A C falls in the range 0 to 12 .

The total cost of production and marketing x units of a product is given by C ( x ) = Rs 1 6 x 3 - 20 x 2 + 25 x + 24 . Find marginal cost and the number of units of the product produced to minimise the marginal cost.

Given, C ( x ) = 1 6 x 3 - 20 x 2 + 25 x + 24 Marginal cost M C = d d x C ( x ) = d d x 1 6 x 3 - 20 x 2 + 25 x + 24 = 1 2 x 2 - 40 x + 25 For marginal cost to be minimum or maximum, d d x M C = 0 d d x ( 1 2 x 2 - 40 x + 25 ) = 0 x - 40 = 0 x = 40 Hence, 40 units must be produced to minimise marginal cost.

EASY

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If the cost function of a production unit is $C (x) = 40 - 20 x + 10 x^{2}$ , find the average cost function and the output $x$ where average cost is minimum. Verify that the average cost is equal to the marginal cost at this level of output.

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Important Questions on Application of Calculus

EASY

Mathematics>Integral Calculus>Application of Calculus>Minimizing average Cost

C (x) = x^{3} - 24 x^{2} + 600 x

, calculate the range where

A C

falls.

EASY

Mathematics>Integral Calculus>Application of Calculus>Minimizing average Cost

C (x) = x^{3} - 24 x^{2} + 600 x

, find the point where

A C = M C

. Verify that

A C

is minimum at this point. What is the minimum average cost ?

MEDIUM

Mathematics>Integral Calculus>Application of Calculus>Minimizing average Cost

The cost function C of a firm is given as

C = 100 x - 10 x^{2} + \frac{1}{3} x^{2} .

Calculate output, at which the average cost is minimum.

EASY

Mathematics>Integral Calculus>Application of Calculus>Minimizing average Cost

The total/cost of production and marketing

x

units of a product is given by

C (x) = Rs (\frac{1}{3} x^{3} - 10 x^{2} + 15 x + 10)

. Find the number of units of the product produced to minimize the average variable cost.

EASY

Mathematics>Integral Calculus>Application of Calculus>Minimizing average Cost

The cost function of a product is

C (x) = 2 x^{2} - 8 x + 50

, where

x

is the number of units produced. In order to minimise the average cost, how many units of the product must be produced.

EASY

Mathematics>Integral Calculus>Application of Calculus>Minimizing average Cost

The cost function of a product is

C (x) = 4 x^{3} - 20 x^{2} + 36 x

, where

x

is the number of units produced. In order to minimise the average cost, how many units of the product must be produced.

EASY

Mathematics>Integral Calculus>Application of Calculus>Minimizing average Cost

The cost function of a product is

C (x) = 4 x^{3} - 64 x^{2} - 900 x

, where

x

is the number of units produced. In order to minimise the average cost, how many units of the product must be produced.

EASY

Mathematics>Integral Calculus>Application of Calculus>Minimizing average Cost

The cost function of a product is

C (x) = 21 x - 12 x^{2} + 3 x^{3}

, where

x

is the number of units produced. In order to minimise the average cost, how many units of the product must be produced.

EASY

Mathematics>Integral Calculus>Application of Calculus>Minimizing average Cost

The cost function of a product is

C (x) = \frac{x^{3}}{3} - 6 x^{2} + 4 x

, where

x

is the number of units produced. In order to minimise the average cost, how many units of the product must be produced.

EASY

Mathematics>Integral Calculus>Application of Calculus>Minimizing average Cost

Find the number of units of the product produced to minimise the marginal cost when the total cost of production and marketing

x

units of a product is given by

C (x) = R s . (\frac{1}{3} x^{3} - 10 x^{2} + 15 x + 30)

EASY

Mathematics>Integral Calculus>Application of Calculus>Minimizing average Cost

The total cost function for $x$ units is given by $C (x) = \sqrt{6 x + 5} + 2500$ .Find the marginal cost.

MEDIUM

Mathematics>Integral Calculus>Application of Calculus>Minimizing average Cost

If $C = 0.01 x^{2} + 5 x + 100$ is the cost function for $x$ items of a product. At what level of production average cost is minimum? What is the minimum average cost?

EASY

Mathematics>Integral Calculus>Application of Calculus>Minimizing average Cost

The cost function of a product is given by

C (x) = \frac{x^{3}}{3} - 45 x^{2} - 900 x + 36

where

x

is the number of units produced. How many units should be produced to minimise the marginal cost?

EASY

Mathematics>Integral Calculus>Application of Calculus>Minimizing average Cost

C (x) = x^{3} - 24 x^{2} + 600 x

, find the point where

A C = M C

. Verify that

A C

is minimum at this point. What is the minimum average cost ?

EASY

Mathematics>Integral Calculus>Application of Calculus>Minimizing average Cost

The total cost of production and marketing x units of a product is given by

C (x) = Rs (\frac{1}{6} x^{3} - 20 x^{2} + 25 x + 24)

. Find marginal cost and the number of units of the product produced to minimise the marginal cost.

EASY

Mathematics>Integral Calculus>Application of Calculus>Minimizing average Cost

The total cost of production and marketing x units of a product is given by

C (x) = Rs (x^{3} - 12 x^{2} + 5 x + 10)

. Find marginal cost and the number of units of the product produced to minimise the marginal cost.

If the cost function of a production unit is C(x)=40-20x+10x2, find the average cost function and the output x where average cost is minimum. Verify that the average cost is equal to the marginal cost at this level of output.

Important Questions on Application of Calculus

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If the cost function of a production unit is $C (x) = 40 - 20 x + 10 x^{2}$ , find the average cost function and the output $x$ where average cost is minimum. Verify that the average cost is equal to the marginal cost at this level of output.