Solve lpp question graphically, Operation Research

Assignment Help:

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.

 


Related Discussions:- Solve lpp question graphically

Linear programming , the application areas of linear programming

the application areas of linear programming

process technolgy, 1 strategic implication of product and process decision...

1 strategic implication of product and process decisions 2 process planning and design 3 work measurement

Maths, Maxz=3x1-2x2 St x1-x2 >_0, 3x1-x2 _0

Maxz=3x1-2x2 St x1-x2 >_0, 3x1-x2 _0

Linear programning, b. A paper mill produces two grades of paper viz., X an...

b. A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y pape

Lpp, A paper mill produces two grades of paper viz., X and Y. Because of ra...

A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i

Question, A paper mill produces two grades of paper viz., X & Y. Because of...

A paper mill produces two grades of paper viz., X & Y. Because of raw material restrictions, it cannot produce more 400 tons of grade X paper & 300 tons of grade Y paper in a week.

Simplex method, Maximize Z =3x+4x subject to x1+x2 =3 2x1+3x2 =4 x1,x2 =0

Maximize Z =3x+4x subject to x1+x2 =3 2x1+3x2 =4 x1,x2 =0

Solve the following Linear Programming Problem using Simple , Solve the fol...

Solve the following Linear Programming Problem using Simple method. Maximize Z= 3x1 + 2X2 Subject to the constraints: X1+ X2 = 4 X1 - X2 = 2

MINIMIZATION., Consider the LP min ?? = 50??1 + 100??2 3 ??.??. 7??1+2??2=2...

Consider the LP min ?? = 50??1 + 100??2 3 ??.??. 7??1+2??2=28 2??1+12??2=24 ??1,??2=0 a. A basic solution of the constraint equations of this problem has how many basic variables,

Linear Programming Problem using Simple method, Solve the following Linear ...

Solve the following Linear Programming Problem using Simple method. Maximize Z= 3x1 + 2X2 Subject to the constraints: X1+ X2 = 4 X1 - X2 = 2 X1, X2 = 0

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd