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A firm manufactures two products; the net profit on product 1 is Rupees 3 per unit and Rupees 5 per unit on product 2. The manufacturing process is such that each product has to be processed in two departments D1 and D2. Each unit of product1 requires processing for 1 minute at D1 and 3 minutes at D2; each unit of product 2 requires processing for 2 minutes at D1 and 2 minutes at D2. Machine time available per day is 860 minutes at D1 and 1200 minutes at D2. How much of product 1 and 2 should be produced every day so that total profit is maximum. Make the mathematical model for the given problem.

Sagot :

To answer this question we need to make use of Linear Programming

The solution is:

x = 170 units

y = 345 units

z(max) = 2235 rupees

To solve a linear programming problem, we need to formulate the model  

The Objective Function

Let´s call x the number of product 1 manufactured

and y the number of product 2 manufactured

Then the Objective Function is:

z = 3× x + 5×y    to be maximize

The set of constraints are:

                              D1           D2

                            ( min. )     ( min. )

Product  1 (x)          1               3

Product 2 (y)          2              2            

Availability            860        1200

First constraint:

Time available in D1:  860 minutes

1×x  +  2×y  ≤ 860

Second constraint:

Time available in D2: 1200 minutes

3×x  +  2×y  ≤ 1200

General constraint:   x ≥ 0  ;  y ≥ 0   integers ( we will assume only complete products at the end of the period no fractions )

Then the model is:

z = 3× x + 5×y    to be maximize

Subject to:  

1×x  +  2×y  ≤ 860

3×x  +  2×y  ≤ 1200

x ≥0   y ≥ 0   integers

With the help of AtoZmath we get the solution:

x = 170 units

y = 345 units

z(max) = 2235 rupies

Related Link: https://brainly.com/question/15319802

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