Question

2. Use matrix algebra to answer the following question: A division of an automobile manufacturing company handles two models: A and B. Model A requires 1 labour hour to paint and 1⁄2 labour hour to polish. Model B requires 1 labour hour for each process. During each hour that the division operates, there are 90 labour hours available for painting and 75 labour hours for polishing. The number of each model that this division must handle if all labour hours available are utilized happens to be

   1. a) 20 of A, 70 of B

   2. b) 50 of A, 40 of B

   3. c) 60 of A, 30 of B

   4. d) 45 of A, 45 of B

   5. e) 30 of A, 60 of B

   6. f) None of the above

be detail explain why .

Answer 1

Model A requires 1 labour hour to paint and 1/2 labour hour to polish

Model B requires 1 labour hour to paint and 1 labour hour to polish

Total number of labour hours available for painting = 90

Total number of labour hours available for polishing =75

Let 'x' & 'y' be the number of model A & model B respectively that the division must handle in order to utilize all the labour hours properly

From the above, we obtain

Total Labour hours required to paint both models = 1 x (x) + 1 x (y) = x+y

Total Labour hours required to polish both models = 1/2 x (x) + 1 x (y) = (x/2)+y

From the above analysis, we equate the total labour hours required to total labour hours available

x + y = 90 & x/2 + y = 75

x = 30

y = 60

Therefore, the number of cars of model A = 30 & the number of cars of model B = 60, which the division must handle if all the available labour hours are to be utilised.

Ans: Option E. 30 of A, 60 of B