Class 12 CBSE A.O.D Exercise 6.9
Class 12 CBSE Applied Maths aims to develop an understanding of basic
mathematical and statistical tools and their
applications in the field of commerce (business/ finance/economics) and social
sciences. Topics covered in Class 12th Applied Maths includes : Numbers, Quantification and
Numerical Applications, Algebra, Calculus, Probability Distributions , Inferential Statistics, Index
Numbers and Time-based data , Financial Mathematics , Linear Programming.
Please Select
Q1.The demand function is x = (24 – 2p)/3, where x is the number of units demanded and p is the price per unit. Find the revenue function R in terms of p.
Solution :
Q2.A publishing house finds that the cost directly attributed to each book is Rs.30
and that the fixed costs are Rs.15000. If each book can be sold for Rs.45, then determine
(i) the cost function
(ii) the revenue function
(iii) the breakeven point
Solution :
Q3.The selling price of a commodity is fixed at Rs.60 and its cost function is C(x)
= 35x + 250
(i) Determine the profit function.
(ii) Find the breakeven point.
Solution :
Q4.A television manufacturer finds that the total cost for the production and
marketing x number of television sets is :
C(x) = 300x^2 + 4200x + 13500
Each product is sold for Rs.8400. Determine the breakeven points.
Solution :
Q5.A firm paid Rs.25000 as the rent of its office and Rs.15200 as the interest of the loan taken to produce x units of a commodity. If the cost of production per unit is Rs.8 and each item is sold at a price of Rs.75, find the profit function. Also, find the breakeven point.
Solution :
Q6.A company sells its product at Rs.10 per unit. The fixed cost for the company is
Rs.35000 and the variable cost is estimated to run 30% of the total revenue. Determine:
(i) the revenue function
(ii) the total cost function
(iii) the number of products the
company must
sell to cover the fixed cost.
Solution :
Q7.A company man function, where a variable cost manufactures wristwatches for which p = 1500 – 3x represents the demand function, where p is the price per unit. Cost price involves initially a fixed cost of Rs.38400 and a cost of Rs.420 per watch. Find at what level of production the company expects to recover its cost.
Solution :
Q8.The fixed cost of a new product is Rs.35000 and the variable cost per unit is Rs.500. If the d function is p = 5000 – 100x, find the breakeven value(s).
Solution :
Q9.A company has a fixed cost of Rs.10000 and the cost of producing one unit of its product is Rs.50. If each unit sells for Rs.75, find the breakeven value. Also, find the values of x for which the company always results in profit.
Solution :
Q10.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 as the cost of production. Find the level of sales at which the company can expect to cover its costs.
Solution :
Q11.TA company sells pens at Rs.5 per unit. The fixed cost for the company is
Rs.3200 and the variable cost is estimated to run 25% of the total revenue. Determine :
(i) the total revenue function,
(ii) the total cost function, (iii) the number of pens points,
and,
(iv) the number of pens the company must sell to cover its fixed cost.
Solution :
Q12.A company sells x packets of noodles each day at Rs.20 a packet. The cost of production is Rs.15 per packet plus a fixed daily overhead cost of Rs.1200. Determine the profit function. What is the profit if 1000 packets are produced and sold every day? 500 packets? 200 packets?
Solution :
Q13.The demand x of a commodity in terms of price p is given by x = 1/9 (245 – 7p).
The average cost is Rs.20 per unit. Find in terms of p:
(i) the cost function,
(ii) the revenue function,
(iii) the profit function, and
(iv)
the price and
level of output at which profit is zero.
Solution :
