tan Step 5 is not required in this situation as exact values of the are known PQ QB I 200 Example 2 Let a business firm produces three types products P P and P that uses three types of raw materials R R and R Let the firm has purchase orders from two clients F and F Considering the situation that the firm has a limited quantity of R R and R respectively prepare a model to determine the quantities of the raw material R R and R required to meet the purchase orders Solution Step 1 The physical situation is well identified in the problem Step 2 Let A be a matrix that represents purchase orders from the two clients F and F Then A is of the form MATHEMATICS A F ot to he Let B be the matrix that represents the amount of raw materials R R and R required to manufacture each unit of the products P P and P Then B is of the form A P B P or 1 h cot B AB Rationalised 2023 24 Step 3 Note that the product which in this case is well defined of matrices A and B is given by the following matrix R R R F F 10 15 6 10 20 0 AB R R R3 which in fact gives the desired quantities of the raw materials R R and R to fulfill the purchase orders of the two clients F and F Example 3 Interpret the model in Example 2 in case 3 40 neters h 1 a and B B 7 9 3 5 12 7 and the available raw materials are 330 units of R 455 units of R Solution Note that 10 15 6 10 20 0 r 793 5 12 7 lied R R3 F 165 247 87 R 140 units of R