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

Operation research, 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

Operations research, six operators are to be assigned to the 5 jobs with th...

six operators are to be assigned to the 5 jobs with the cost of assignments

Transportation, we have three reservoirs with daily supplies of15, 20 and 2...

we have three reservoirs with daily supplies of15, 20 and 25 litres of fresh water respectively. on each day we must supply four cities A B C D whose demands are 8 10 12 and 15 res

OR models, Explain why it may be advantageous to build models to help in so...

Explain why it may be advantageous to build models to help in solving a decision problem.

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

35mm slider -report writing presentation , 35mm Slider  35 mm Slider l...

35mm Slider  35 mm Slider like OHP transparencies casts  an images but they  have different  uses and  properties. They are used  to show an actual photographic  images in the

Answer, A paper mill products two grade of paper viz., X & Y. Because of ra...

A paper mill products two grade of paper viz., X & Y. Because of raw material restriction, it cannot produce more than 400 tons of grade X paper & 300 tons of grade Y paper in a we

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

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

#title.L.L.p, #use the simple method to solve the following L.P.P. Maximi...

#use the simple method to solve the following L.P.P. Maximize Z =4X1 +10X2 subject to constraints, 2X1 +X2 2X1+5X2 2X1 +3X2 X1,X2 > 0

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