Since
product P1 requires 3 units of R1, P2 requires 7 units of R1 and P3 requires 5 units of R1
(observe matrix B) and the total number of units, of R1, available is 330, we have
3x + 7y + 5z = 330 (for raw material R1)
Similarly, we have
4x + 9y + 12z = 455 (for raw material R2)
and
3y + 7z = 140 (for raw material R3)
This system of equations can be expressed in matrix form as
3
7
5
4
9
12
0
3
7
330
455
140















=








x
y
z
Rationalised 2023-24
202
MATHEMATICS
Step 3 Using elementary row operations, we obtain
1
0
0
0
1
0
0
0
1
20
35
5















=








x
y
z
This gives x = 20, y = 35 and z = 5 Thus, the firm can produce 20 units of P1, 35
units of P2 and 5 units of P3 to make full use of its available raw material Remark One may observe that if the manufacturer decides to manufacture according
to the available raw material and not according to the purchase orders of the two
clients F1 and F2 (as in Example 3), he/she is unable to meet these purchase orders as
F1 demanded 6 units of P3 where as the manufacturer can make only 5 units of P3 Example 5 A manufacturer of medicines is preparing a production plan of medicines
M1 and M2