BUSINESS MATHEMATICS (B.COM-HONOURS)
APPLICATION OF MATRICES TO BUSSINESS AND ECONOMICS
QUESTIONS ASKED IN DELHI UNIVERSITY IN FINAL EXAMINATION
(Q.NO-1) Mr. A went market to purchase 3kg of sugar, 10kg of wheat and 1kg of salt. In a shop
near to Mr. a residence, these commodities are priced at Rs.20, Rs.10 and Rs.8 per kg whereaeas in
local market these commodities are priced at Rs.15, Rs.8 and Rs.6 per kg respectively. If cost of
travelling to local market is Rs.25, find the net savings of Mr. a using matrix multiplication
method. A three sector economy has the following input-output coefficient matrix (in quantity).
(Q.NO-2) The labour days required per unit of output of the three sectors are 0.4, 0.7 and 1.2
respectively and their consumer output targets are 1000, 5000 and 4000 units respectively. The
wage rate is Rs.10 per Labour Day. By using matrix algebra you are required to find:
1. The gross output of each sector
2. Total labour days required
3. Equilibrium prices and
Total value added.
(Q.NO-3) A firm has two machines M1 and M2 costing Rs.45, 000 and Rs. 30, 000. Each has 5
years life with scrap value nil. Find depreciation of each machine for each year using matrix
notations if:
a. Both are depreciated by sum -of-the-years’ digit method,
b. First is depreciated by sum-of-the-years’ digits method and second by straight line
method.
(Q.NO-4) A firm produces three products p1, p2and p3 processed on four machines M1, M2, M3
AND M4 M1 can process 25 units of p1or 50 units of p2 or 75 units of p3 per hour. M2can process
50 units of p3 per hour. M2 can process 50 units of any product per hour. M3 can process 50 or 25
or 100 units per hour and machine M4 can process 50 or 40 or 50 units per hour of P1, P2 and P3
respectively. The processing hour available on the machines M1, M2, M3 and M4 are 12, 12, 13,
and 13 respectively. Usine matrices, find how many units of three products can be produced with
the unavailable time fully used?
(Q.NO-5)A hypothetical economy produces only two commodities X and Y. The two commodities
serve as intermediate inputs in each others production. To produce a unit X 0.2 unit x and 0.6 unit
of Y are needed. To produce a unit of Y, 0.4 unit of X and 0.3 unit of y are needed. Three and five
labour hours are required to produce a unit of X and unit of Y respectively .The wage rate is Rs: 20
BUSINESS MATHEMATICS (B.COM-HONOURS)
per labour hour. If the final demand of X increases by 150 units and that of Y decreases by 120
units, find:
1. Change in the gross output of each of the two commodities;
2. Change in labour requirement;
3. Change in the value-added in the two producing sectors.
(Q.NO-6) In an engineering workshop there are 10 machines for drilling, 8 machines for turning
and 7 machines for grinding. Three types of brackets are made. Types I bracket require 0 minutes
for drilling, 5 minutes for turning and 4 minutes for grinding. The corresponding timing for the II
and type III brackets is 3, 3, 2 and 3, 2, 2 minutes respectively.
How many brackets of each type can be produced so that all the machines remain fully occupied
during an hour? Solve by using matrix algebra.
(Q.NO-7) you are given the input-output matrix of a closed model with three sectors below:
I
II
III
I
0.1
0.2
0.2
II
0.6
0.2
0.4
0.3
0.6
0.4
III
If the output of the 1 sector is 100 crores of rupees, find the equilibrium outputs of IInd and IIIrd
sectors.
(Q.NO-8) The purchase price of MARUTI Zen car is Rs. 4, 40,000. The rate of cost of repair is
given by:
C=22,000(1-𝐞 −𝟎.𝟓𝒍)
Where t represent the years of use since purchase. Find the cumulative repair cost at the end of 5
years. (1- 𝒆−𝟎.𝟓𝒍=0.7788)
(Q.NO-9) A country produces only two goods X and Y. The two commodities serve as intermediate
inputs in each other’s production. 0.1 units of X and 0.2 units of Y are needed to produce a unit of
Y. In addition to this 4 units and 3 units of primary input are needed to produce each unit of X and
Y respectively.
I.
II.
III.
If 240 and 140 units of X and Y respectively are needed for final consumption, find gross
output levels of the two goods.
If the price of primary input is Rs. 10 per unit, cumpute the prices of the goods.
Also compute total value added.
BUSINESS MATHEMATICS (B.COM-HONOURS)
(Q.NO-12) The following matrix gives the proportionate mix of constituent used for three
fertilizers.
FERTILIZERS
A
0.5
B
0
C
0.5
D
0
0.2
0.3
0
0.5
0.2
0.2
0.1
0.5
I
II
III
I.
II.
If sales are 1,000 tines (of one kilogram) per week, 20% being fertilizer 2 and 50% being
fertilizer 3, how much does one kilogram tin of each fertilizer cost?
If the cost of each constituent is 50 paise 60 paise, 75 paise and 100 paise per 100 grams
respectively, how much does one kilogram tin of each fertilizer cost?
(Q.NO-13) To control a crop disease it is necessary to use 8 units of chemical A, 14 units of
chemical B 13 units of chemical C. One barrel of spray P contains are unit of A, 2 units of B
and 3 units of C. One barrel of spray Q contains 2 units of A, 3 units of B and 2 units