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

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

Experimental method, In this method variables beings studied are contro...

In this method variables beings studied are controlled by the investigator. In other the effect of one variable is observed while other relevant variables are held constant

Decision Analysis, make a research project for modern day companies on how...

make a research project for modern day companies on how they can make decisions using decision analysis

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

Do it - report writing presentation , Do it  Everything  about  the...

Do it  Everything  about  the presentation is  ready and so  are you. The only  things  left if to face the audience in a confident and positive  manner and leave a mark on

Operations strategy in an organization, 1. Investigate: The Operations Str...

1. Investigate: The Operations Strategy of your organisation or one you are familiar with and answer the following points. Does your chosen organisation have an operations

Scope, Scope of operation research?

Scope of operation research?

Quality circles, advantage of quality circle process

advantage of quality circle process

Techniques of operations research, There is no unique set of problems which...

There is no unique set of problems which can be solved by using operations Research Models r techniques. Several operations Research Models or techniques can be grouped into some b

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