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

TRANSPOTATION, LIMITS OF TRANSPOTATION PROBLEM

LIMITS OF TRANSPOTATION PROBLEM

Research analysis and project, Scenario: You work as a junior employee i...

Scenario: You work as a junior employee in the marketing department of a medium-sized Hong Kong organisation. One of your major tasks is your involvement in your organization's

Modeling, Model building is the essence of the operations research approach...

Model building is the essence of the operations research approach? Discuss.

Linear Programming , A Paper mill produces two grades of paper viz. X and ...

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 in

Uncertainly, Uncertainly : There is a great uncertainly about economic a...

Uncertainly : There is a great uncertainly about economic and general environment. With economic growth uncertainty is also growing's. this makes each decisions costlier

Linear programming, #questiA paper mill produces two grades of paper viz X ...

#questiA 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 pa

Simple method, solve the LPP using simple method, maximize z= 3x1+2x2 subje...

solve the LPP using simple method, maximize z= 3x1+2x2 subject to constraints

Software, role of computer software operation research

role of computer software operation research

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

B 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

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