PQ h tan= = or 1 = h cot QB 1 Step 5 is not required in this situation as exact values of the are known. he eters h, I, a and Example 2 Let a business firm produces three types of 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 F2. 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 F2. Then, A is of the form ot to rece . . A = F. . and 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, P2 and P3. Then, B is of the form B = P R R R, = P 200 MATHEMATICS 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 R2 R3 F AB= F 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. 1 Example 3 Interpret the model in Example 2, in case [10 15 6 A = 3 4 0 B=793 10 200 5 12 7 and the available raw materials are 330 units of R,, 455 units of R Solution Note that NOORT Jed 10 20 R 0 793 5 12 7 R2 R3 E[165 247 87] 140 units of R.