Page 63 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes
300
Let, B = 300
300

0.7 1 3.2 300 1470
Then, AB = 2 4 6 300 3600
1 1.5 2 300 1350

Thus the requirement is: 1470 c.ft. of timber, 3600 dozens of nails and 350 litres of varnish.

Example
In a certain city, there are 50 colleges and 400 schools. Each school and college have 18 Peons, 5
Clerks and 1 Cashier. Each college in addition has one Section Officer and one Librarian. The
monthly salary of each of them is as follows:

Peon: 1,200; Clerk: 2,000; Cashier: 2,400; Section Officer: 2,800 and Librarian: 3,600. Using
the matrix notation, find (i) total number of posts of each kind in schools and colleges taken
together, (ii) the total monthly salary bill of all the schools and colleges taken together.

Solution:
The number of posts of each kind in a school or a college can be written as a column vector.
(i) The total number of posts of each kind, in schools and colleges taken together, can be
written as column matrix P, as shown below, where the first and second column vectors
give the number of posts of each kind in a school and a college respectively.

18 18 7200 900 8100 Peons
5 5 2000 250 2250 Clerks
P = 400 1 50 1 400 50 450 Cashiers
0 1 0 50 50 S.Officers
0 1 0 50 50 Librarians

(ii) Salaries for different posts can be written as row matrix S, as shown below:
S = [1200 2000 2400 2800 3600]

8100
2250
Total salary bill = SP = [1200 2000 2400 2800 3600] 450
50
50

= 1200 × 8100 + 2000 × 2250 + 2400 × 450 + 2800 × 50 + 3600 × 50
= 1,56,20,000.
Example 15.
A firm produces three products A, B and C, which it sells in two markets. Annual sales in units
are given below:
Units Sold
Market A B C
I 8000 4000 16000
II 7000 18000 9000

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