The marginal revenue of selling x units of a commodity is given by M R = 20 e x / 10 1 + x 10 . If the revenue obtained on selling 10 units of the commodity is Rs 200 e , find the revenue function.

M R = 20 e x 10 ( 1 + x 10 ) Revenue function R ( x ) = ∫ M R d x R ( x ) = ∫ 20 e x 10 ( 1 + x 10 ) d x R ( x ) = 20 [ 10 e x 10 + x e x 10 - 10 e x 10 ] + k R ( x ) = 20 x e x 10 + k Also, given R ( 10 ) = 200 e 20 x e x 10 + k = 200 e 200 e + k = 200 e k = 0 Hence, R ( x ) = 20 x e x 10

EASY

12th ICSE

IMPORTANT

Earn 100

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.

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 5

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.

MEDIUM

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Application of Calculus in Commerce and Economics>EXERCISE>Q 6

The marginal revenue of selling x units of a commodity is given by

M R = 20 e^{x / 10} (1 + \frac{x}{10})

. If the revenue obtained
on selling

10

units of the commodity is Rs

200 e

, find the revenue function.

EASY

12th ICSE

IMPORTANT

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

The cost function

C (x)

for x breads is given by

C (x) = (3.5 x + 12000)

. If each bread is sold for

6

, determine the minimum number of breads that should be produced and sold to ensure no loss.

EASY

12th ICSE

IMPORTANT

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

The cost function

C (x)

for

x

breads is given by

C (x) = (3.5 x + 12000)

. If the selling price is

R s 6.5

per bread, what would be the break-even point?

EASY

12th ICSE

IMPORTANT

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

A factory is manufacturing table fans. From the information given below, calculate the breakeven point (of cost).
Total fixed cost

= 30 l a c s

Cost of labour per fan

= 30

Cost of material per fan

= 275

Miscellaneous variable expenses per fan

= 45

Selling price per fan

= 500

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Application of Calculus in Commerce and Economics>CHAPTER TEST>Q 3

An entrepreneur wants to start the production of floppy disks. He observes that he will have to spend

2

lacs for technical know-how,

6

lacs on plant and machinery, and the cost of producing each floppy is

6

. He can sell each floppy at

13

. Determine the break-even point. Also calculate his profit or loss when he produces

1

lac floppy disks.

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Application of Calculus in Commerce and Economics>CHAPTER TEST>Q 3

An entrepreneur wants to start the production of floppy disks. He observes that he will have to spend

2

lacs for technical know-how,

6

lacs on plant and machinery, and the cost of producing each floppy is

6

. He can sell each floppy at

13

. Determine the break-even point. Also calculate his profit or loss when he produces

1.5

lacs floppy disks.

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Application of Calculus in Commerce and Economics>CHAPTER TEST>Q 4

A firm knows that demand function for its main product is linear. It also knows that it can sell

3000

units at

5

per unit and it can sell

1200

units when price is

11

per unit. Determine the demand function.

The marginal cost of product is given by MC=5002x+25 and the fixed cost is Rs.2500 Find the total cost function. Also find the average cost of producing 72 units.

Important Questions on Application of Calculus in Commerce and Economics

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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.