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 ) .

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 revenue function in terms of p .

Demand function = 1 9 ( 245 - 7 p ) Revenue function = price × demand function R ( x ) = p × 1 9 ( 245 - 7 p ) = p 9 ( 245 - 7 p ) Hence, revenue function is p 9 ( 245 - 7 p ) .

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 profit 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 ) Demand function = 1 9 ( 245 - 7 p ) Revenue function = price × demand function R ( x ) = p × 1 9 ( 245 - 7 p ) = p 9 ( 245 - 7 p ) Profit function P ( x ) = R ( x ) - C ( x ) P ( x ) = p 2 ( 245 - 7 p ) - 20 2 ( 245 - 7 p ) = ( p - 20 ) 2 ( 245 - 7 p ) Hence, profit function is 1 2 ( 245 - 7 p ) ( p - 20 ) .

EASY

12th ICSE

IMPORTANT

Earn 100

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.

Important Questions on Application of Calculus in Commerce and Economics

EASY

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

EASY

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.

EASY

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)

EASY

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?

EASY

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

EASY

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 revenue function in terms of

p

EASY

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 profit function in terms of

p

The price of selling one unit of a product when x units are demanded is given by the equation p=4000-2x. 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.

Important Questions on Application of Calculus in Commerce and Economics

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