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

Ques, Ask questb. A Company produces 150 cars. But the production rate vari...

Ask questb. A Company produces 150 cars. But the production rate varies with the distribution. Production Rate 147 148 149 150 151 152 153 Probability 0.05 0.10 0.15 0.20 0.30 0.15

A paper mill produces, . A paper mill produces two grades of paper viz., X ...

. 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

Find the maximum and minimum values, Problems based on solution of a given ...

Problems based on solution of a given LPP when it has multiple optimal solution: 1.    Find the maximum and minimum values of 5x+2y, subject to the constraints -2x-3y ≤ -6

Observation and data collection - research phases, Observation and Data Col...

Observation and Data Collection for Better Understanding of the Problem: Many times actual observations by trained observers at the scene of operation may be difficult and da

TRANSPOTATION, LIMITS OF TRANSPOTATION PROBLEM

LIMITS OF TRANSPOTATION PROBLEM

Semeter 5, explian completelly the operation reserch

explian completelly the operation reserch

Determining sample size for estimating means-sample decisons, Determining S...

Determining Sample Size for estimatingMeans a. Acceptable Errors: There  may be several errors  in the  sample  size. The researcher  will have  to decide those  errors. Whic

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

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