Solve lpp question graphically, Operation Research

A producer of furniture manufactures two products - tables and chairs. Processing of these products is done on two machines A and B. A chair needs 2 hours on machine A and 6 hours on machine B. A table needs 5 hours on machine A and no time on machine B. There are 16 hours of time per day accessible on machine A and 30 hours on machine B. Profit earned by the manufacturer from a chair and a table is Rs 2 and Rs 10 correspondingly. What must be the everyday production of each of two products?

Answer

Assume x1 indicates the number of chairs

Assume x2 indicates the number of tables

 

Chairs

Tables

Availability

Machine A

Machine B

2

6

5

0

16

30

Profit

Rs 2

Rs 10

 

 

LPP

Max Z = 2x1 + 10x2

Subject to

2x1+ 5x2 ≤ 16

            6x1 + 0x2 ≤ 30

 x1 ≥ 0 , x2 ≥ 0 

 

Solve graphically

The first constraint 2x1+ 5x2 ≤ 16, can be written in the form of equation

2x1+ 5x2 = 16

Place x1 = 0, then x2 = 16/5 = 3.2

Place x2 = 0, then x1 = 8

The coordinates are (0, 3.2) and (8, 0)

The second constraint 6x1 + 0x2 ≤ 30, can be written in the form of equation

6x1 = 30 → x1 =5

764_LPP Problems Solved Graphically.png

The corner positions of feasible region are A, B and C. So the coordinates for the corner positions are

A (0, 3.2)

B (5, 1.2) (Solve the two equations 2x1+ 5x2 = 16 and x1 =5 to obtain the coordinates)

C (5, 0)

 

We are given that Max Z = 2x1 + 10x2

At A (0, 3.2)

Z = 2(0) + 10(3.2) = 32

 

At B (5, 1.2)

Z = 2(5) + 10(1.2) = 22

 

At C (5, 0)

Z = 2(5) + 10(0) = 10

 

Max Z = 32 and x1 = 0, x2 = 3.2

The manufacturer must manufacture about 3 tables and no chairs to obtain the max profit.

 

Posted Date: 7/4/2012 3:42:54 AM | Location : United States







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