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 model, formulate the linear programming model of the tab...

formulate the linear programming model of the table above

Scope of operations research, Scope of the OR techniques can be derived ...

Scope of the OR techniques can be derived in followings various importance fields: 1. In Agriculture : With the explosion of population and consequent shortage of food O

.sequencing problem, which job should proceed first among the 2 jobs on n ...

which job should proceed first among the 2 jobs on n machines by graphical method

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

Question, A paper mill produces two grades of paper viz., X & Y. Because of...

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.

Deweys principle - information resources, Dewey's Principle: Melvil De...

Dewey's Principle: Melvil Dewey's principle states: "The best reading for the largest number at the least cost" According to this principle a library should select, within the

Deviation taken from assumed mean, Deviation Taken from Assumed Mean ...

Deviation Taken from Assumed Mean This methods  is assorted  when the  arithmetic  average  is a  fractional value. Taking  deviation from  fractional value would  be a ver

Linear Programming Problem, A paper mill produces two grades of paper viz. ...

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

Lpp, A paper mill produces two grades of paper viz., X and Y. Because of ra...

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

Microforms and photographs - classification of documents, Photographs and I...

Photographs and Illustrations: Photographs and illustrations are documents which provide a visual or pictorial representation of a person, place or situation which words fail

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