Use matrix algebra to answer the following question: A division of an automobile

Question

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 ½ 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

a) 20 of A, 70 of B
b) 50 of A, 40 of B
c) 60 of A, 30 of B
d) 45 of A, 45 of B
e) 30 of A, 60 of B
f) None of the above

can i know the reason and the process please.

Explanation / Answer

Model A takes 1 hour to paint and 0.5 hour to poilish.

Model B takes 1 hour to paint and 1 hour to polish.

Total painting hours = 90 hours

Total polishing hours= 75 hours

Now, from this given information,

Let' a' is the model A automobiles and 'b' is the model B automobiles.

Now, a+ b = 90

and 0.5 a + b = 75

by solving both equations we get,

a/2 = 15

a= 30

Therefore, b = 90-30 =60

So, the model A = 30 automobiles and model B = 60 automobiles.

Hence Option (e) is the correct answer.

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