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

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

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

Introduction to probability distribution , Introduction to Probability Dist...

Introduction to Probability Distribution By  theoretical distribution we mean  a frequency distribution  which  is obtained  in relation to a random  variable by some  mathem

Regression, Regression line drawn as Y=C+1075x, when x was 2, and y was 239...

Regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual

Closed lood, give the procedure of tracing a closed loop

give the procedure of tracing a closed loop

Drurys principles, Drury's Principles: The basic principle, which stil...

Drury's Principles: The basic principle, which still governs the selection of reading material for a library, was enunciated by Drury  in 1930. It states: "To provide the righ

Sample linear programming problems to calculate max profit, The following l...

The following linear programming is written to plan the production of two products. And the company wants to maximize profits. x1 = number of product 1 produced in each batch

Game theory, if there were n workers and n jobs there would be

if there were n workers and n jobs there would be

Steps of field study, Festinger and Katz have described followings six ste...

Festinger and Katz have described followings six steps in the conduct to a field study. a. Preliminary Planning :Deciding scope and objectives of study and the time table

Determining sample size for estimating poportions, Determining Sample Size ...

Determining Sample Size for Estimating poportions It is  necessary  to determining  the sample size for a  problem involving  proportions. This deals  with the percentage of f

Chi square test goodness of fit- hypothesis testing, Chi Square  Test Good...

Chi Square  Test Goodness of Fit Chi square test  can be used to find out  how well the  theoretical distribution fit  with the  empirical distribution  of observed distribut

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