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

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

Linear programming, A paper mill produces two grades of paper viz., X and Y...

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

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

Conclusions and recommendations , Conclusions and Recommendations  Con...

Conclusions and Recommendations  Conclusions  should  be drawn with  direct  reference to the objectives  of the study. The  readers should  be able  to read the objectives. T

Policies, POLICIES, NORMS AND STANDARDS: Information source; building,...

POLICIES, NORMS AND STANDARDS: Information source; building, an important function of the library, should be based on sound policies and programmes.  The basic question of

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

Help, A paper mill produces two grades of paper viz., X and Y. Because of r...

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

PROBLEM , #A paper mill produces two grades of paper viz., X and Y. Because...

#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

Scattered responsibility and authority, Scattered Responsibility and Autho...

Scattered Responsibility and Authority: In a big industry responsibility and authority of decisions making is scattered throughout the organization and thus the organization.

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