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

Dina, Construct a two-variable LP model that: · Maximizes Z; · ...

Construct a two-variable LP model that: · Maximizes Z; · All coefficients in the objective function are greater than 500; · Includes at least 5 constraints;

Big M method, Maximize p = (3)x + 2y subject to 2x + y 3x + 4y >= 12

Maximize p = (3)x + 2y subject to 2x + y 3x + 4y >= 12

Multiple objectives- sampling decisions, Multiple  Objective s The sam...

Multiple  Objective s The sample  may vary according  to the  objective of the research. There  may several objectives  of marketing  research so the  sample  size  may vary a

Poisson Process, Telephone calls arrive at a switchboard in a Poisson proce...

Telephone calls arrive at a switchboard in a Poisson process at the rate of 2 per minute. A random one-tenth of the calls are long distance. (a) What is the probability of at least

SIMPLEX METHOD, Solve the following Linear Programming Problem using simple...

Solve the following Linear Programming Problem using simple method Maximize Z= 3x1 + 2x2 Subject to the constraints: X1 + X2 = 4

Game theory , 3 In a rectangular game, pay-off matrix of player A is as f...

3 In a rectangular game, pay-off matrix of player A is as follows:

Discuss how theories is helpful researchers in communication, QUESTION 1 ...

QUESTION 1 i) What do you understand by the following terms? And what is their role in communication theories? Ontology Epistemology Axiology ii) Discuss how

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