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

Linear programming , Solve the following Linear Programming Problem using S...

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

Integer programming, An integer programming problem is identical to a linea...

An integer programming problem is identical to a linear programming problem except that one or more decision variables are constrained to take integer values. Such problems cannot

Rephrasing the research problem, Rephrasing the Research Problem Final...

Rephrasing the Research Problem Finally as a researcher you should rephrase the research problem. Once you have followed all the four steps above, i.e., 1) You have clear

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

De, describe the similarities and differences of transportation and linear ...

describe the similarities and differences of transportation and linear programing methods

DECISION MODELS, CRITICAL EXAMINATION OF THE APPLICATION OF DECISION THEORY...

CRITICAL EXAMINATION OF THE APPLICATION OF DECISION THEORY TECHNIQUES OR MODEL IN BUSINESS DECISION MAKING IN NIGERIA

Expected value analysis, Profitable Casino Corp. (PCC) is a Harrah's wannab...

Profitable Casino Corp. (PCC) is a Harrah's wannabe, intent on mimicking Harrah's analytical marketing techniques.  For example, PCC issues virtually all gamers a PCC "Rewards" car

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

Duality, For every LP formulation there exists another unique linear ...

For every LP formulation there exists another unique linear programming formulation called the 'Dual' (the original formulation is called the 'Primal'). Same data

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