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

LPP, USE SIMPLE METHOD TO SOLVE THE FOLLOWING LPP MAXIMISE Z=4X1+10X2 SUBJE...

USE SIMPLE METHOD TO SOLVE THE FOLLOWING LPP MAXIMISE Z=4X1+10X2 SUBJECT TO CONSTRAINS, 2X1+X2 2X1+5X2 2X1+3X2 X1, X2>0

Assignment question. please give me the solution, A paper mill produces two...

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

Some guidelines for bibliography entries , Some Guidelines  for Bibliograp...

Some Guidelines  for Bibliography Entries 1. Reference of a Back  by One Authors : Mention authors  name book title ( in italics hence  to be  underlined) city  publication

Sequential sampling -sampling decisons, Sequential Samplin The previou...

Sequential Samplin The previous  has shown  that the sampling  units  were drawn  prior  to the drawing of the actual   sample  and has  a fixed  size. But the  sequential  sa

Experimental design and methodology , Case Study - Experimental Design ...

Case Study - Experimental Design Dental Clinic A leading dental clinic  with  three well qualified  dentists is seriously  considering  keeping  in touch  with  its  pat

Pay-off matrix , In a rectangular game, pay-off matrix of player A is as fo...

In a rectangular game, pay-off matrix of player A is as follows: Player B B1 B2 Player A A1 A2 i) Solve the game. ii) Write down the pay-off matrix of B and th

Solve by computational procedure of big – m method, Example 2 Max Z = 3...

Example 2 Max Z = 3x 1 - x 2 Subject to             2x 1 + x 2 ≥ 2             x 1 + 3x 2 ≤ 3             x 2 ≤ 4     &     x 1 ≥ 0, x 2  ≥ 0   A

Linear programing, Maximize6x1+8x2+5x3,st,labour3x1+4x2+5x3 =0 then brefly ...

Maximize6x1+8x2+5x3,st,labour3x1+4x2+5x3 =0 then brefly explain x1,x2,x3;term labour,metal&plastic;the160hours;x1,x2&x3>=0

process technolgy, 1 strategic implication of product and process decision...

1 strategic implication of product and process decisions 2 process planning and design 3 work measurement

Oral presentation - report writing presentation, Oral Presentation At ...

Oral Presentation At times  oral presentation of the  results of the study is considered effective particularly in case where  policy recommendations are indicated by project

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