Q13 of 45 Page 250

A company manufactures two types of screws A and B. All the screws have to pass through a threading machine and a slotting machine. A box of Type A screws requires 2 minutes on the threading machine and 3 minutes on the slotting machine. A box of type B screws requires 8 minutes of threading on the threading machine and 2 minutes on the slotting machine. In a week, each machine is available for 60 hours.

On selling these screws, the company gets a profit of Rs 100 per box on type A screws and Rs 170 per box on type B screws.


Formulate this problem as a LPP given that the objective is to maximise profit.

Let the company manufactures x boxes of type A screws and y boxes of type B screws. We make the following table from the given data:



Thus according to the table, the profit becomes, Z=100x+170y


Now, we have to maximize the profit, i.e., maximize Z=100x+170y


The constraints so obtained, i.e., subject to the constraints,


2x+8y≤ 3600 [time constraints for threading machine]


Now will divide throughout by 2, we get


⇒ x+4y≤ 1800…………..(i)


And 3x+2y≤3600 [time constraints for slotting machine]


⇒ 3x+2y≤3600…………..(ii)


And x≥0, y≥0 [non-negative constraint]


So, to maximize profit we have to maximize Z=100x+170y subject to


x+4y≤ 1800


3x+2y≤3600


x≥0, y≥0


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