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Question
A firm manufactures two types of products A and B and sells them at a profit of Rs 2 on type A and Rs 3 on type B. Each product is processed on two machines M1 and M2. Type A requires one minute of processing time on M1 and two minutes of M2; type B requires one minute on M1 and one minute on M2. The machine M1 is available for not more than 6 hours 40 minutes while machine M2 is available for 10 hours during any working day. Formulate the problem as a LPP.
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Solution
Let the firm produces x units of product A and y units of product B.
Since, each unit of product A requires one minute on machine \[M_1\] and two minutes on machine \[M_2\] Therefore, x units of product A will require product x minutes on machine \[M_1\] and 2x minutes on machine \[M_2\]
Also,
Since each unit of product B requires one minute on machine \[M_1\] and one minute on machine \[M_2\] Therefore, y units of product A will require product y minutes on machine \[M_1\] and y minutes on machine \[M_2\]
It is given that the machine \[M_1\] is available for \[6 \text{ hours and 40 minutes} \] i.e. 400 minutes and machine \[M_2\] is available for 10 hours i.e. 600 minutes
\[2x + y \leq 600\]
Hence, the required LPP is as follows:
Maximize Z = 2x + 3y
subject to \[x + y \leq 400\]
\[2x + y \leq 600\]
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