Linear programming solution by steps for two-phase method, Operation Research

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

Posted Date: 7/8/2012 12:36:46 AM | Location : United States







Related Discussions:- Linear programming solution by steps for two-phase method, Assignment Help, Ask Question on Linear programming solution by steps for two-phase method, Get Answer, Expert's Help, Linear programming solution by steps for two-phase method Discussions

Write discussion on Linear programming solution by steps for two-phase method
Your posts are moderated
Related Questions
the following table gives place under different states of nature Strategies States of nature s1 s2 s3 A 10000 3000 2000 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 i

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

Regression Line The line  of regression  is the  line  which give the best  estimate  to the  values  of one  variable  for any  specific  values  of other  variable. For t

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

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

Normal 0 false false false EN-IN X-NONE X-NONE

1. Investigate: The Operations Strategy of your organisation or one you are familiar with and answer the following points. Does your chosen organisation have an operations

regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual

Maximize Z= 3x1 + 2X2 Subject to the constraints: X1+ X2 = 4 X1 - X2 = 2 X1, X2 = 0 on..