ML Aggarwal Applications of Calculus in Commerce and Economics ISC Class-12 APC Maths

ML Aggarwal Applications of Calculus in Commerce and Economics ISC Class-12 Understanding APC Maths Solutions Chapter-1 of Section-C. Step by step Solutions of ML Aggarwal ISC Understanding APC Mathematics Class-12 Exercise Questions with Chapter Test. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

ML Aggarwal Applications of Calculus in Commerce and Economics ISC Class-12 APC Maths

Class: 12th
Subject: Mathematics
Chapter : Ch-1 Applications of Calculus in Commerce and Economics  Section-C
Board ISC Board
Writer ML Aggarwal ISC Understanding ( Vol-II)
 Publications APC Arya Publications ( 2020-21 )

-: Select Topics :-

Exe-1.1, 

Exe-1.2, 

Exe-1.3, 

Exe-1.4, 

Chapter Test


ML Aggarwal Applications of Calculus in Commerce and Economics ISC Class-12 APC Maths

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.

Revenue function:

Revenue means the amount received by a company by selling a certain number of units of a commodity. Let p be the price per unit and x be the number of units sold. Then total revenue
R or R(x) = p . x
If price p is constant, then R(x) is obviously a straight line. If price p varies with demand
x, then p = f (x) so that
R or R (x) = (demand) . (price) = x f (x)

BREAKEVEN ANALYSIS:

Usually, as the companies incur capital costs (fixed costs), they are in loss when the production/sale is low. However, as the production/sale increases, the average cost comes down, and beyond a certain point, the company starts making profit. This leads us to breakeven point analysis. The breakeven point is the level of production where the revenue from sales is equal to the total cost of production. At this point, the company makes neither profits nor losses.


Exercise – 1.1,

ML Aggarwal Applications of Calculus in Commerce and Economics ISC Class-12 APC Maths

(page-1426)

Question 1: For manufacturing a certain item, the find out cost is 6500 ………………… 12.50.

Question 2: The cost function for a certain …………………………. when 3 units are produced.

Question 3: ……………………..

……………………

Question 4: The total cost of producing and marketing x unit of commodity is given by C ………………………………..

…………………


Exercise – 1.2,

ML Aggarwal Applications of Calculus in Commerce and Economics ISC Class-12 APC Maths

(page-1431 to 1432)

Question 1: Find the profit and hence find the breakeven points when :

(i)……………

Question 2: A publishing house ……………………. the breakeven point.

Question 3: ………………….

…………………….

Question 14: The demand x of a commodity in term of price  p is given by ……………………….. term of p:

…………………..


Exercise – 1.3,

ML Aggarwal Applications of Calculus in Commerce and Economics ISC Class-12 APC Maths

(page-1442 to 1444)

Question 1: A manufacture’s total cost function is C = 1200 + 20x + x² Find

(i)……………

Question 2: Given the total cost of function for x units of a ommodity as …………………….. average cost function.

Question 3: …………………..

……………………..

Question 21: Find the profit maximizing  output level, given x = 200 ………………………… AC is the average cost.


Exercise – 1.4,

ML Aggarwal Applications of Calculus in Commerce and Economics ISC Class-12 APC Maths

(page-1446)

Question 1: The marginal cost of manufacturing x unit of product is given by ……………………. Find the total cost and the average cost.

Question 2: The marginal cost function …………………………………. and the average cost.

Question 3: …………………………….

……………………………….

Question 6: The marginal revenue of selling x unit of commodity is given by MR -………………………………….  find the revenue of function.


Chapter Test

ML Aggarwal Applications of Calculus in Commerce and Economics ISC Class-12 APC Maths

(page-1447)

Question 1: The cost function c (x) for  x bread is given by c(x) = ………………

(i)……………….

Question 2: A factory is ………………………………………    Selling  price per fan = 500.

Question 3: ……………………..

……………………..

Question 10: If the marginal revenue of function of commodity ……………………. find the demand function.

-: End of Applications of Calculus in Commerce and Economics  ML Aggarwal ISC Class-12 Solutions :-

Return to :- ML Aggarwal ISC Class-12 APC Understanding Maths Solutions


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