Question:Using Simplex iteratively

Question:Using Simplex iteratively

Maple

Dear Maple friends,

I have the following problem: after solving LP1, I want to find the values of this solution. And with this solution, replacing in LP1--  I obtain a new LP problem  called LP2. I want to solve these steps  in an efficient way. I am still using Maple 10.

[ LP1: ]

Max  alpha

subject to

x1  +  x2 + x3                                +    alpha  >= 95

x1 + x2           +x4                         +    alpha  >= 85

x1        + x3  + x4                          + alpha  >= 80

x2  + x3  + x4                           + alpha >= 55

x1 +x2                              +alpha >= 50

x1 + x3                             + alpha >= 50

x1 + x4                             + alpha >= 50

x2 + x3                             +alpha >= 50

x2 + x4                             + alpha >= 50

x3 + x4                             + alpha >= 50

x1                                      + alpha >= 0

x2                                      + alpha >=0

x3                                      + alpha >=0

x4                                        +alpha >=0

x1 + x2+ x3 + x4                                         =100

x1                                                                    >=0

x2                                                                   >=0

x3                                                                   >=0

x4                                                                    >=0

[end of the problem]

Solving the previous problem,we obtain a solution of the kind:

alpha = 10

x3 = 23

x4 = 15

x1>=30

x2>=  25

x1+x2 =60

Replacing (the solution x3=25 and x4 = 15, x1+x2 =60 and simplifying) in the previous problem we obtain a new version of problem LP1

LP_2a

Minimize   alpha2

subject to

x1 + alpha2 >=40

x2+alpha2 >=15

x1+alpha2 >= 25

x1+alpha2 >=35

x2+ alpha2 >=25

x2 + alpha2>=35

x1+x2 =60

x1 >= 30

x2 >= 25

I can simplify even more to obtain

[SECOND PROBLEM]

LP2

Min  alpha2

subject to:

x1 + alpha1  >=40

x2 + alpha1 >=  35

x1+x2 =60

x1>=30

x2>=25

SOLUTION:  alpha2 = 7.5,  x1= 32.5,  x2= 27.5

The problem is:  Starting with LP1, how can I solve LP2 in an efficient way?. I will need to do this kind of "iterated" application of simplex, considering several steps: LP1, LP2..LP12, and several times. Then.. I dont want to do by hand.

Regards,

Jean-Jacques

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