Linear programming solution by steps for two-phase method, Operation Research

Assignment Help:

Solve by Steps for Two-Phase Method

Max Z = 5x1 + 8x2

Subject to

3x1 + 2x2 ≥ 3

x1 + 4x2 ≥ 4

x1 + x2 ≤ 5

    &     x1 ≥ 0, x≥ 0

Answer

Standard LPP

 

Max Z = 5x1 + 8x2  

    Subject to

                        3x1 + 2x2 - s1+ a1 = 3

                        x1 + 4x2 - s2+ a2  = 4

                        x1 + x2 + s3 = 5

                        x1 , x2 , s1, s2, s3, a1, a≥ 0

 

Auxiliary LPP

Max Z* = 0x1 + 0x2 + 0s1 + 0s2 + 0s3 -1a1 -1a2

    Subject to

                        3x1 + 2x2 - s1+ a1 = 3

                        x1 + 4x2 - s2+ a2  = 4

                        x1 + x2 + s3 = 5

                        x1 , x2 , s1, s2, s3, a1, a≥ 0

1377_two-steps-method-LPP.png

 

As all Δj ≥ 0, Max Z* = 0 and no artificial vector appears in the basis, we move to phase II. 

Phase II

266_phase-II.png

As all Δj ≥ 0, optimal basic feasible solution is achieved. Thus the solution is Max Z = 40, x1 = 0, x2 = 5


Related Discussions:- Linear programming solution by steps for two-phase method

Graphical method- minimization example, Minimization Example  A ...

Minimization Example  A farmer is advised to utilize at least 900 kg of mineral A and 1200 kg of mineral B to increase the productivity of crops in his fields.

Linear programming problem, Solve the following Linear Programming Problem ...

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

Linear Programming , A paper mill produces two grades of paper viz., X and ...

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 pa

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

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

Institutional Characteristics - information resources, Institutional Charac...

Institutional Characteristics:  An approach to an understanding of the fields of interest of individuals to be served and of the organisation as a whole could begin by acquiri

Determination of the operation, An operation is a combination of different...

An operation is a combination of different actions dealing with raw materials( e, g, men and machines) which form a structure from which an action with regard to broader ob

Modi method, find optimal solution for a 3*4 matrix 42 27 24 35 46 37 32 3...

find optimal solution for a 3*4 matrix 42 27 24 35 46 37 32 32 40 40 30 35 using modi method

Cross cultural communication in the workplace, This assignment requires you...

This assignment requires you to carry out the first part of a research project on the topic of "Cross cultural communication in the workplace". You can take any approach to this to

Linear Programming models, In your own words, describe the special cases of...

In your own words, describe the special cases of integer programming and binary programming: what makes these problems different? Give an example of each, pointing out why they mus

Linear programming problem, a paper mill prodecs two grades of paper viz., ...

a paper mill prodecs 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 in

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