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 programing, Solve the following Linear Programming Problem using Sim...

Solve the following Linear Programming Problem using Simple method. Maximize Z= 3x1 + 2X2

LPP, A paper mill prouduces two grads of paper viz., X and Y. Becouse of ra...

A paper mill prouduces two grads of paper viz., X and Y. Becouse of raw material restriction, it cannot product more then 400 tons of grade X paper and 300 tons of grade Y paper in

Linear programing, Solve the following Linear Programming Problem using Sim...

Solve the following Linear Programming Problem using Simple method. Maximize Z= 3x1 + 2X2 Subject to the constraints: X1+ X2 = 4 X1 - X2 = 2 X1, X2 = 0

Linear Programming, 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

Identifying the solution to a problem, Software House named as Harvester, g...

Software House named as Harvester, got to increase the speed of service and I need to get 3000 words written

Assignment answer, Q2.Six Operators are to be assigned to five jobs with th...

Q2.Six Operators are to be assigned to five jobs with the cost of assignment in Rs. given in the matrix below. Determine the optimal assignment. Which operator will have no assignm

MODI method, explain the procedure of MODI method of finding solution throu...

explain the procedure of MODI method of finding solution through optimaly test.

LPP, a paper mill produce two grades of paper viz., X and Y. because of raw...

a paper mill produce two grades of paper viz., X and Y. because of raw material restrictions, it cannot produce more than 400 tona of grade X and 300 tons of grade Yin a week. ther

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

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