Step 2 Let A be a matrix that represents purchase orders from the two clients F1 and
F2 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