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

Determine phases-states-decisions and probability , G. Ambler has € 10000 ...

G. Ambler has € 10000 available for a second hand car, but would like to buy a fast car that costs € 25000. He needs the money for that car quickly, and would like to increase his

Quality circles, advantage of quality circle process

advantage of quality circle process

Hypothesis building and testing, Hypothesis  Building and Testing The...

Hypothesis  Building and Testing The foundation of hypothesis building  lies in discovering links between  elements  of your data. CAQDAS can help you to  discover these links

International trade, why does south africa regulate int''l trade

why does south africa regulate int''l trade

Sequencing, how the sequencing techniques help the manager

how the sequencing techniques help the manager

Model., is model the essence of oprational research.

is model the essence of oprational research.

Linear programing, A factory employs unskilled workers earning $135 per wee...

A factory employs unskilled workers earning $135 per week and skilled workers earning $270 per week. It is required to keep the weekly age bill below $24,300. The machine requires

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