Then, A is of the form
1
2
3
1
2
P P
P
F •
•
•
A
F
•
•
•


=




Let B be the matrix that represents the amount of raw materials R1, R2 and R3,
required to manufacture each unit of the products P1, P2 and P3 Then, B is of the form
1
2
3
1
2
3
•R R R
•
•
P
B
P
•
•
•
P
•
•
•




=






Rationalised 2023-24
200
MATHEMATICS
Step 3 Note that the product (which in this case is well defined) of matrices A and B
is given by the following matrix
1
2
3
1
2
R R R
F •
•
•
AB F
•
•
•


=




which in fact gives the desired quantities of the raw materials R1, R2 and R3 to fulfill
the purchase orders of the two clients F1 and F2 Example 3 Interpret the model in Example 2, in case
3
4
0
10
15
6
A =
, B
7
9
3
10
20
0
5
12
7






=










and the available raw materials are 330 units of R1, 455 units of R2 and 140 units of R3 Solution Note that
AB =
3
4
0
10
15
6
7
9
3
10
20
0
5
12
7



 


 


 



=
R
R
R
F
F
1
2
3
1
2
165
247
87
170
220
60




This clearly shows that to meet the purchase order of F1 and F2, the raw material
required is 335 units of R1, 467 units of R2 and 147 units of R3 which is much more than
the available raw material