A manufacturer's marginal cost function is 500 2 x + 25 . Find the cost involved to increase production from 100 units to 300 units.

Marginal cost is the derivative of the cost function. ∴ C ( x ) = ∫ M ( x ) dx = ∫ 500 2 x + 25 dx Let 2 x + 25 = t ⟹ 2 dx = dt ∴ C ( x ) = ∫ 250 t dt C ( x ) = 500 ( t ) + c = 500 ( 2 x + 25 ) + c C ( 100 ) = 500 ( 225 ) + c = 7500 + c C ( 300 ) = 500 ( 625 ) + c = 12500 + c C ( 300 ) - C ( 100 ) = 5000 Therefore, cost involved to increase production from 100 units to 300 units is 5000 .

The cost function for a certain commodity is C ( x ) = 12 + 3 x - 1 3 x 2 Write down the total cost, fixed cost, variable cost and average cost when 3 units are produced.

Given, cost function C ( x ) = 12 + 3 x - 1 3 x 2 When x = 3 Total cost = 12 + 3 ( 3 ) - 3 2 3 = 18 Fixed cost means no units are produced i.e. x = 0 Fixed cost = 12 Variable cost = Total cost - Fixed cost = 18 - 12 = 6 Avearge cost = Total cost Number of units = 18 3 = 6 Hence, total cost is ₹ 18 , fixed cost is ₹ 12 , variable cost is ₹ 6 and average cost is ₹ 6 .

Given the total cost function for x units of a commodity as C ( x ) = 1 3 x 3 + x 2 - 8 x + 5 , find slope of average cost function.

Given, cost function C ( x ) = 1 3 x 3 + x 2 - 8 x + 5 Average cost function A C = Total cost Number of units A C = 1 3 x 3 + x 2 - 8 x + 5 x A C = 1 3 x 2 + x - 8 + 5 x Slope of average cost function = d d x ( 1 3 x 2 + x - 8 + 5 x ) = 2 3 x + 1 - 5 x 2 Hence, Slope of average cost function is 2 3 x + 1 - 5 x 2 .

EASY

Earn 100

The marginal cost (MC) of a product is given to be a constant multiple of the number of units $(x)$ produced .Find the total cost function, if fixed cost is $R s . 5000$ and the cost of producing $50$ units is $R s . 5625$ .

50% studentsanswered this correctly

Important Questions on Application of Calculus

EASY

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

A manufacturer's marginal cost function is

\frac{500}{\sqrt{2 x + 25}}

. Find the cost involved to increase production from

100

units to

300

units.

EASY

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

A company sells its products at the rate of

R s 6

per unit. The variable costs are estimated to run

25 %

of the total revenue received. If the fixed costs for the product are

R s 4500

, find the total cost function.

HARD

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

The marginal cost function

M C = 2 + 5 e^{x}

, find average cost function, when

x = 0, C = 100

EASY

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

The marginal cost function of producing

x

units of a product is given by

M C = 3 x^{2} - 10 x + 3 .

If the total cost of producing

1

unit of the product is

6

, find the total cost function and the average cost.

EASY

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

The marginal cost function of producing x units of a product is given by

M C = 3 e^{0.3 x} + 5

. If the fixed cost is Rs.

6050,

find the total cost function. Also find the cost of production of

10

units.

EASY

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

The cost function for a certain commodity is

C (x) = 12 + 3 x - \frac{1}{3} x^{2}

Write down the total cost, fixed cost, variable cost and average cost when

3

units are produced.

HARD

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

The marginal cost function of manufacturing

x

shoes is

6 + 10 x - 6 x^{2}

. The cost producing a pair of shoes is

12

rupees. Find the total and average cost function.

MEDIUM

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

The monthly marginal cost for a product is

M C = x + 30

. If fixed cost is

50

rupees, find the total cost function for the month.

EASY

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

Cost of producing

75

units of a commodity is

275

and cost of producing

150

units is

300

. Assuming that TC is linear, find the cost function.

EASY

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

Given the total cost function for

x

units of a commodity as

C (x) = \frac{1}{3} x^{3} + x^{2} - 8 x + 5

, find slope of average cost function.

EASY

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

The marginal cost function of a product is given by

M C = \frac{2}{\sqrt{4 x + 9}}

. If the fixed cost is

Rs 540

, find the total cost function. Also find the average cost of producing

4

units of the product.

EASY

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

For manufacturing a certain item, the fixed cost is

6500

and the cost of producing each unit is

12.50

. What is the cost function? Draw a graph, clearly indicating TC, TFC and TVC.

EASY

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

The marginal cost of manufacturing x units of a product is given by

M C = x^{2} — 150 x + 750

. If the fixed cost is

1250

, find the total cost and the average cost.

HARD

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

The marginal cost function

M C = 2 + 5 e^{x}

, find

C if C (0) = 100

EASY

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

The marginal cost of product is given by

M C = \frac{500}{\sqrt{2 x + 25}}

and the fixed cost is Rs.

2500

Find the total cost function.

EASY

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

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.

MEDIUM

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

A manufacturer can sell

x

items of commodity at a price of

Rs . (330 - x)

each. Find the revenue function along with the cost of producing

x

items is

Rs . (x^{2} + 10 x + 12)

, determine the profit function.

EASY

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

The marginal cost function of producing x units of a product is given by

M C = 3 e^{0.3 x} + 5

. If the fixed cost is Rs.

6050,

find the total cost function. Also find the cost of production of

10

units.

EASY

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

Cost of producing

75

units of a commodity is

275

and cost of producing

150

units is

₹ 300

. Assuming that TC is linear, find the average total cost of producing

75, 150, 225

units respectively.

EASY

Mathematics>Integral Calculus>Application of Calculus>Determination of Cost Function

The marginal cost of product is given by

M C = \frac{500}{\sqrt{2 x + 25}}

and the fixed cost is Rs.

2500

Find the total cost function. Also find the average cost of producing

72

units.

The marginal cost (MC) of a product is given to be a constant multiple of the number of units (x) produced .Find the total cost function, if fixed cost is Rs.5000 and the cost of producing 50 units is Rs.5625.

Important Questions on Application of Calculus

Learn and Prepare for any exam you want !

The marginal cost (MC) of a product is given to be a constant multiple of the number of units $(x)$ produced .Find the total cost function, if fixed cost is $R s . 5000$ and the cost of producing $50$ units is $R s . 5625$ .