Question

A firm manufactures two types of products P1 and P2. Each product is processed on two machines A and B. Type Pi requires 2 minutes of processing time on A and one minute on B; type P2 requires 3 minutes on A and 2 minutes on B. Machine A is available for 7 hours 30 minutes while machine B is available for 12 hours during any working day. Formulate the problem as an LPP if he sells them on a profit of 3 OMR on type P and 2 OMR on type P Then. the objective function to maximize the profit is Z= Note: Use the variables x and y.

Answer 1

Given: A firm produces two products P1 and P2 processed on two machines for different times.

To find: Formulate the problem as LPP.

Solution:

Let required production of product P1 and P1 be x and y respectively.

Since profit on each product P1 and P2 are 3 units and 2 units respectively. So, profits on x number of type P1 and y number of type P2 are 3x and 2y respectively.

Let Z denotes total profit, so,

Z = 3x + 2y which is the objective function and this has to maximized.

Let us find the constraints.

Since, P1 requires 2 minutes on machine A and P2 requires 3 minutes on A. So, x of type P1 and y of type P2 require 2x and 3y minutes respectively. But,

Total time available on machine A is 7 hours 30 minutes = 450 minutes.

So,

2x + 3y has to be less than or equal to 450

2x + 3y ≤ 450 {First Constraint}

Since, P1 requires 1 minute on machine B and P2 requires 2 minutes on B. So, x of type P1 and y of type P2 require x and 2y minutes respectively. But,

Total time available on machine B is 12 hours = 720 minutes.

So,

x + 2y has to be less than or equal to 720.

x + 2y ≤ 720  {Second Constraint}

Hence mathematical formulation of the given LPP is,

Maximize, Z = 3x + 2y

Subject to constraints,

2x + 3y ≤ 450

x + 2y ≤ 720

Also, x,y ≥  0 [Since production of P1 and P2 cannot be less than zero]

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