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 M_{1} and M_{2}. Type A requires one minute of processing time on M_{1} and two minutes of M_{2}; type B requires one minute on M_{1} and one minute on M_{2}. The machine M_{1} is available for not more than 6 hours 40 minutes while machine M_{2} is available for 10 hours during any working day. Formulate the problem as a LPP.

Asked by Sakshi | 1 year ago | 98

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, M_{1}

One unit of product B requires 1minutes on machine, M_{1}

So,

x unit of product A requires 1x minutes on machine, M_{1}

y unit of product B requires 1y minutes on machine, M_{1}

Total minutes on M_{1} = 2000 minutes

i.e., x + y ≤ 400

Second constraint:

Given:

One unit of product A requires 2minutes on machine, M_{2}

One unit of product B requires 1minutes on machine, M_{2}

So,

x unit of product A requires 2x minutes on machine, M_{2}

y unit of product B requires 1y minutes on machine, M_{2}

Total minutes on M_{2} = 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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