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?


Assume x1 indicates the number of chairs

Assume x2 indicates the number of tables





Machine A

Machine B








Rs 2

Rs 10




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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