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

Operations research, state phases of operations research and and their impo...

state phases of operations research and and their importance in solving problems

Operation research, types of OR ,technique and mathematical system and line...

types of OR ,technique and mathematical system and linear programming system in operation research

Assigment , b. A paper mill produces two grades of paper viz., X and Y. Bec...

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 pape

Yates correction for continuity for 2x 2tables , Yates Correction for Cont...

Yates Correction for Continuity for  2x 2Tables If any cell frequency in  2x 2 table isles  than 5thenfor the application of X 2 test it  is pooled with the preceding or suc

Validity of the model - operation research model, Deriving the Solution fro...

Deriving the Solution from the Model: This phase is devoted to the computation of those value of decision variables that maximize or minimize the objective function. Such

Mccolvin''s principles, McColvin's Principles: L.R McColvin advanced h...

McColvin's Principles: L.R McColvin advanced his Demand and Supply Theory of Book Selection in 1925. He states, "Books in themselves are nothing. They have no more meaning tha

Find out where you should now invest your money, Question : Suppose tha...

Question : Suppose that you want to invest $10000 in the stock market by buying shares in one of two companies: A and B. Shares in Company A are risky but could yield a 50% ret

Production option and the ato process design, The plant is using the chase ...

The plant is using the chase production option and the ATO process design. The BOM is illustrated below.   Requirement The factory works on a process layout but

Lpp linear programming problems exercise, Exercise Define the t...

Exercise Define the terms used in LPP. Mention the advantages of LPP. What are the assumptions and limitations of LPP? A firm produces three pro

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

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