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, x2  ≥ 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, a2  ≥ 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, a2  ≥ 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

Short question, write down any two assumption of L.P

write down any two assumption of L.P

Components included in the reseach proposal, Components Included in the Pro...

Components Included in the Proposal Personnel In case the proposal is addressed to the funding agencies, the qualifications of the key project personnel for study should be

International trade, why does south africa regulate int''l trade

why does south africa regulate int''l trade

Cost, Six Operators are to be assigned to five jobs with the cost of assign...

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 assignment

Inventory models - techniques of operations research, Inventory models deal...

Inventory models deal with the problem of determination of how much to order at a point in time and when to place an order. The main objective is to minimize the sum of three

Determine phases-states-decisions and probability , G. Ambler has € 10000 ...

G. Ambler has € 10000 available for a second hand car, but would like to buy a fast car that costs € 25000. He needs the money for that car quickly, and would like to increase his

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

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

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

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

Uncertainly, Uncertainly : There is a great uncertainly about economic a...

Uncertainly : There is a great uncertainly about economic and general environment. With economic growth uncertainty is also growing's. this makes each decisions costlier

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

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