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 DRUG MANUFACTURER produces 2 products X1 and X2.X1 ne...

A DRUG MANUFACTURER produces 2 products X1 and X2.X1 needs 2 hours on machine A AND 2 HOURS ON MACHINE B.X2 needs 3 hours on machine A and 1 hour on machine B.If machine A can run

Model, Importance of models

Importance of models

Evolution, how did operation research evolve

how did operation research evolve

Network problem, Consider the following network where the value on each arc...

Consider the following network where the value on each arc represents the capacity of that arc. Use the augmenting path algorithm to find the value of the maximum flow from node 1

Manner of presentation - report writing presentation, Manner of Presentatio...

Manner of Presentation  Decide  whether  you wish  to achieve  your  objective by a formal  presentation or a  non formal  type  of presentation. As  discussed  earlier 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

Making decision - hypothesis testing, Making Decision Lastly a deci...

Making Decision Lastly a decision  should  be arrived as to whether the null  hypothesis is  to be accepted  or rejected. In  this regard the value  of the test  statistic

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