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.
Now, let x and y be the required production of products A and B.
Given:
Profit on one unit of product A is = Rs 2
So, profit on x unit of product A = 2x
Profit on one unit of product B is = Rs 3
So, profit on x unit of product B = 3y
Let total profit be ‘Z’
So, Z = 2x + 3y
First Constraint:
Given:
One unit of product A requires 1minutes on machine, M1
One unit of product B requires 1minutes on machine, M1
So,
x unit of product A requires 1x minutes on machine, M1
y unit of product B requires 1y minutes on machine, M1
Total minutes on M1 = 2000 minutes
i.e., x + y ≤ 400
Second constraint:
Given:
One unit of product A requires 2minutes on machine, M2
One unit of product B requires 1minutes on machine, M2
So,
x unit of product A requires 2x minutes on machine, M2
y unit of product B requires 1y minutes on machine, M2
Total minutes on M2 = 2500 minutes
i.e., 2x + y ≤ 600
Hence, the required mathematical formulation of linear programming is:
Maximize Z = 2x + 3y
Subject to x + y ≤ 400
2x + y ≤ 600
Where, x, y ≥ 0
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