Page 117 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes
1 5 z
5 15 z 15 z 25 5z 4z 10 10 4z
y =
3 3 3 3

Since we can assign infinite number of values to z, there are infinite number of solutions.
Since the variables are not permitted to be negative, we can write.

z 5
x = 0 or z ³ –5
3

10 4z 5
and y = 0 or 10 – 4z ³ 0 or z
3 2

5
Since z cannot be negative, therefore the range of values of z is restricted to 0 z .
2

Example
Two companies A and B are holding shares in each other, A is holding 20% shares of B and B is
holding 10% shares of A. If the separately earned profits of the two companies are 98,000 and
49,000 respectively, find total profit of each company using matrix algebra. Also show that the
total profits allocated to the outside shareholders is equal to the total of separately earned
profits.
Solution:

Let x and y denote the total profit of the two companies A and B respectively.
Then we can write
x = 98000 + 0.2y or x – 0.2y = 98000
y = 49000 + 0.1x or –0.1x + y = 49000
Writing the above equations as the matrix equation

1 0.2 x 98000
=
0.1 1 y 49000
This can be solved either by matrix inversion method or Cramer’s rule.
Using Cramer’s Rule, we get

98000 0.2
49000 1 107800.00
x = 1,10,000
1 0.2 0.98
0.1 1

1 98000
0.1 49000 58800.00
y = 60,000
0.98 0.98

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