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

Linear Programming, A paper mill produces two grades of paper viz., X & Y. ...

A paper mill produces two grades of paper viz., X & Y. Because of raw material restrictions, it cannot produce more 400 tons of grade X paper & 300 tons of grade Y paper in a week.

Que, #queSix Operators are to be assigned to five jobs with the cost of ass...

#queSix Operators are to be assigned to five jobs with the cost of assignment in Rs. given in the matrix below. Determine the optimal assignment. Which operator will have no assign

Research methodology, Research Methodology 1. Discuss how the researc...

Research Methodology 1. Discuss how the research will be executed to achieve the proposed research objectives. The methodology should be based on the methods that are used in

Examine the future sustainability of business, In your role as a Consultant...

In your role as a Consultant to a renowned organisation or institution, you have been asked to design and submit a research proposal to examine the future sustainability of its bus

Operation research, Model building is the essence of operation research app...

Model building is the essence of operation research approach. Comment

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

A paper mill produces two grades of paper viz., X & Y. Because of raw material restrictions, it cannot produce more 400 tons of grade X paper & 300 tons of grade Y paper in a week.

Formulation of relevant hypotheses and models, Tentative explanations when ...

Tentative explanations when formulated as propositions are called hypotheses. It is very important to state the hypothesis and its anticipated consequences before star

Operation research, Discuss the methodology of operation research

Discuss the methodology of operation research

Linear programming model, Nass food produces to kinds of popular dark choco...

Nass food produces to kinds of popular dark chocolate bars. The banana and the coffee.the

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

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