OP Malhotra **Application of Calculus in Commerce and Economics** ISC Class-12 Maths Solutions Ch-26. Step by step Solutions of OP Malhotra SK Gupta, Anubhuti Gangal S.Chand ISC Class-12 Mathematics with Exe-26(a), Exe-26(b), Exe-26(c), Exe-26(d), Exe-26(e), Exe-26(f), Self Revision and Chapter Test. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

## OP Malhotra Application of Calculus in Commerce and Economics ISC Class-12 Maths Solutions Ch-26

Class: | 12th |

Board | ISC |

Subject: | Mathematics |

Chapter : | Ch-26 Application of Calculus in Commerce and Economics of Section -C |

Topics | Exe-26(a), Exe-26(b),Exe-26(c), Exe-26(d), Exe-26(e), Exe-26(f), Self Revision Chapter Test |

Writer | OP Malhotra, SK Gupta, Anubhuti Gangal |

Publications | S.Chand Publications 2020-21 |

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** Application of Calculus in Commerce and Economics **

**OP Malhotra ISC Class-12 Maths Ch-26**

**Application of calculus in commerce and economics:-**

**Calculus**helps us in finding the rate at which one such quantity changes with respect to the other. Marginal analysis in

**Economics**and

**Commerce**is the most direct

**application**of differential

**calculus**.

**Introduction:**

Quantitative techniques and mathematical models are now being increasingly used in business and economic problems. Differential calculus is used while determining the rate of change of a given function (dependent variable) due to change in one of the independent variables. Integration is the inverse of differentiation and it involves finding a function whose rate of change is given. In this chapter, we shall start with the a few basic concepts of economics—fixed and variable cost, average cost, revenue, profit etc., and then go on to marginal functions (marginal cost and marginal revenue) using first derivative. We shall use second derivatives to find minimum costs and maximum revenue or maximum profit.

**Demand function:**

Various economic studies show that the quantity demanded of a commodity depends upon many factors, viz., price of the commodity, consumer’s income, taste of the consumer, price of other related commodities etc. To simplify things, we will consider the relationship between demand and price of the commodity only, assuming that all other factors remain constant.

**Breakeven Analysis:**

### Exe-26(A),

**OP Malhotra Application of Calculus in Commerce and Economics ISC Class-12 Maths Solutions Ch-26**

Question 1: (i) A manufacturing of steel Almirahs has fixed costs of …………….. producing 100 almirahs?

(ii) A hotel banquets for group of people at a cost of …………. catering for x people.

(iii) ………………..

Question 2: Suppose the cost to produce some commodity is given by p = 1000 ………….. 5000 350 units.

Question 3: A manufacturing can sell ……………. determine the profit functions.

Question 4:

………………………

Question 14: The pricing policy of a company follows the demand function p = d (x). D (x) being the price per unit when ……………….. company expect to recover its costs ?

### Exe-26(B),

Application of Calculus in Commerce and Economics ISC Class-12 Maths Solutions Ch-26

Question 1: Find (a) the average cost and (b) the marginal cost given that for x units of commodity.

(i)……………..

Question 2: (i) If the total cost function for …………. cost function

(ii) The cost of producing x unit of a product is given by …………… cost is always constant.

Question 3: (i) The cost function C(x) of a function …………………….. when x = 2

(ii) The cost function of a firm is given by ……………… when x = 3

(iii) The cost function of a firm is ……………… when x = 3.

Question 4:

…………………….

Question 13: The total function for x units is given by ……………….. as the output x increase.

### Exe-26(C),

OP Malhotra Application of Calculus in Commerce and Economics ISC Class-12 Maths Solutions Ch-26

Question 1: The demand for a certain product is represent by the equation p = 20 ……………….. 2 units are sold.

Question 2: (i) The demand function of a …………… function.

(ii) If P = …………….. revenue function

(iii) If p ……….. find the marginal revenue.

Question 3: The total revenue received from the sale ………………….. selling 50 item.

Question 4:………………….

………………………..

Question 10: For the demand function p ……………………………. with the increase of x.

### Exe-26(D),

Application of Calculus in Commerce and Economics ISC Class-12 Maths Solutions Ch-26

Question 1: The demand function for a manufacturing product is p ………….. What is the maximum revenue ?

Question 2: The unit demand function is cx = 1/3 ………. the revenue is maximum.

Question 3: The demand function for a particular ………….. total revenue is maximum.

Question 4: ……………………

……………………….

Question 20: Given a quadratic cost function C(x) = ………… marginal cost at that value.

### Exe-26(E),

OP Malhotra Application of Calculus in Commerce and Economics ISC Class-12 Maths Solutions Ch-26

Question 9: Given that the marginal cost MC and the average cost AC of a …………. producing 4 unit is 64 rupee.

### Exe-26(F),

OP Malhotra Application of Calculus in Commerce and Economics ISC Class-12 Maths Solutions Ch-26

Question 1: (i) The marginal revenue …… the sale of 100 units

(ii) Find the total revenue ………. 10x + 100.

(ii9i) A manufacturing marginal ………… 400 to 900 units

Question 2: If the marginal revenue function is given ………. when the price is 2.20 rupee.

Question 3: Find the total revenue function and the demand function function for the following revenue functions.

………..

Question 4: ……………

Question 9: A frim’s marginal revenue function ids given by MR ……… a, b, c are constant.

### Self Revision

Application of Calculus in Commerce and Economics ISC Class-12 Maths Solutions Ch-26

Question 1: A company is selling a certain product ………. per unit determine.

Question 2: Given the total cost function for x unit ……… average cost function.

Question 3: A frim has the following total cost and demand functions :

……… maximizing output.

Question 4: ………..

Question 13: The demand function is x = ………………… which the revenue is maximum.

### Chapter Test

OP Malhotra Application of Calculus in Commerce and Economics ISC Class-12 Maths Solutions Ch-26

Question 1: For the first year the fixed cost for setting up a new electronic ……… 270 per calculator.

Question 2: If the cost function C(x) of producing x quantities of ……………… the break-even point ?

Question 3: A company producing dry cells introduces production bonus …………. cell to guarantee no loss ?

Question 4: …………….

Question 12: The average cost of manufacturing 5000 pens is 70 rupee ……… and the average cost function.

**-: End of Application of Calculus in Commerce and Economics ****S. Chand ISC Class-12 Maths Solution :-**

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