The Trix Manufacturing Co. Ltd. produces four products-A, B, C and D. Each product is made from three raw materials- P, Q and R:

PRODUCT MATERIAL A 8 c D p Q R Production data R 2 4 To (per unit) E 5 3 Q 5 3 u 4 2 4 2 R

E s

$ $ $ $ $ $ $

Raw material cost (per unit) 2 3 6 Direct production cost

(per unit) 4 2 3 5 Producer selling price 40 40 36 32 Weekly demand (per unit) 400 500 600 200 REQUIRED

(a) Prepare the following matrices:
W-4 x 3 matrix giving component requirements X -1 x 4 matrix giving weekly demand for each product Y- 3 x 1 matrix giving unit raw material cost Z-4 x 1 matrix giving direct production cost per unit for each product.
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(b) Identify the matrices required to calculate the raw material cost per product and calculate them using matrix methods

(c) Using your result in (b), identify the other matrices you require to calculate the total weekly contribution, and determine the result

(d) Without making the calculations, what interpretation would you give to the matrix T where T =XWY?
ACA. PE, Section 2, Paper 12, Management Mathematics, June 1978