The demand x of a commodity in terms of price p is given by x = 1 9 ( 245 - 7 p ) . The average cost is R s . 20 per unit. Find the cost function in terms of p .

Average cost = R s 20 Average cost = Total cost Number of units Total cost = Average cost × Number of units 20 × 1 9 ( 245 - 7 p ) = C ( x ) C ( x ) = 20 9 ( 245 - 7 p ) Hence, cost function in terms of p is 20 9 ( 245 - 7 p ) .

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12th ICSE

IMPORTANT

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A company manufactures wristwatches for which $p = 1500 - 3 x$ represents the demand function, where $p$ is the price per unit of $x$ units. Cost price initially involves a fixed cost of $Rs 38400$ , and a variable cost of $Rs 420$ , per watch. Find the level of production at which the company expects to recover its cost.

Important Questions on Application of Calculus in Commerce and Economics

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12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Application of Calculus in Commerce and Economics>EXERCISE>Q 10

A company has fixed cost of

Rs 10000

and cost of producing one unit of its product is

Rs 50

. If each unit sells for

Rs 75

, find the break-even value. Also, find the values of

x

for which the company always results in profit.

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IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Application of Calculus in Commerce and Economics>EXERCISE>Q 11

The price of selling one unit of a product when

x

units are demanded is given by the equation

p = 4000 - 2 x

. The fixed costs of the product are

Rs 20000

and

Rs 1484

per unit are paid for the product to place in a store. Find the level of sales at which the company can expect to cover its costs.

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12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Application of Calculus in Commerce and Economics>EXERCISE>Q 12

A company sells pens at

Rs 5

per unit. The fixed cost for the company is

Rs 3200

and variable cost is estimated to run

25 %

of the total revenue. Determine the total revenue function

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12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Application of Calculus in Commerce and Economics>EXERCISE>Q 12

A company sells pens at

Rs 5

per unit. The fixed cost for the company is

Rs 3200

and variable cost is estimated to run

25 %

of the total revenue. Determine the total cost function.

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12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Application of Calculus in Commerce and Economics>EXERCISE>Q 12

A company sells pens at

Rs 5

per unit. The fixed cost for the company is

Rs 3200

and variable cost is estimated to run

25 %

of the total revenue. Determine the break-even point. (Up to two places of decimal)

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12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Application of Calculus in Commerce and Economics>EXERCISE>Q 12

A company sells pens at

R s . 5

per unit. The fixed cost for the company is

R s . 3200

and variable cost is estimated to run

25 %

of the total revenue. Determine the quantity the company must sell to cover its fixed cost.

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Application of Calculus in Commerce and Economics>EXERCISE>Q 13

A company sells x packets of noodles each day at

R s 20

a packet. The cost of production is,

R s . 15

per packet together with a fixed daily overhead cost of

R s . 1200

. Determine the profit function. What is the profit if

1000

packets are produced and sold everyday ? What are the profits for

500

packets and

200

packets respectively?

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12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Application of Calculus in Commerce and Economics>EXERCISE>Q 14

The demand

x

of a commodity in terms of price

p

is given by

x = \frac{1}{9} (245 - 7 p)

. The average cost is

R s . 20

per unit. Find the cost function in terms of

p

Important Questions on Application of Calculus in Commerce and Economics

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