(Manufacturing problem) A manufacturing company makes two models A and B of a product. Each piece of Model A requires 9 labour hours for fabricating and 1 labour hour for finishing. Each piece of Model B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs 8000 on each piece of model A and Rs 12000 on each piece of Model B. How many-pieces of Model A and Model B should be manufactured per week to realise a maximum profit? What is the maximum profit per week?

Explanation

Solution:

Suppose x is the number of pieces of Model A and y is the number of pieces of
Model B. Then
Total profit (in Rs) =`8000 x +12000 y`

Let Z=`8000 x+12000 y`

We now have the following mathematical model for the given problem.

Maximise Z=`8000 x+12000 y ldots (1)`

subject to the constraints :

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