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, x2  ≥ 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, a2  ≥ 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, a2  ≥ 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

Operations function - information system, The Operations Function has alway...

The Operations Function has always relied heavily on information for its smooth running. During this course information has been introduced as one of the five inputs to the convers

What do you understand by the term operations research, Question : (a) ...

Question : (a) (i) What do you understand by the term "operations research"? (ii) Discuss three common operations research models. (b) Self-service at the university c

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

Methodology of operation research, The systematic methodology developed f...

The systematic methodology developed for an operation research study with problems involving conflicting multiple objective policies and alternatives. Operation research in

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

Calculation of standard deviation - discrete series, Calculation  of Stand...

Calculation  of Standard Deviation - Discrete Series   There are three methods for  calculating  standard  deviation  in discrete series": a. Actual Mean Methods: It inc

Investigate and examine aspects of planning structure, You are required to ...

You are required to investigate and examine aspects of planning and organisational structure for a 'real-life' organisation. This assessment enables you to relate the theories and

35mm slider -report writing presentation , 35mm Slider  35 mm Slider l...

35mm Slider  35 mm Slider like OHP transparencies casts  an images but they  have different  uses and  properties. They are used  to show an actual photographic  images in the

Techniques of observation method, Techniques of Observation Method Obs...

Techniques of Observation Method Observation always involves some interaction between respondent and researcher in which researcher has an opportunity to watch respondent fu

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