Linear Programming-Transportation Simplex

[tobinator250]

I don't know if I've posted this in the right place but I thought I'd give it a go anyway.

Homework Statement

See Attatchment

Homework Equations

The Attempt at a Solution

So for part a) max z:150X₁₁+350X₁₂+300X₁₃+100X₂₁+500X₂₂+400X₂₃

s.t. X₁₁+X₁₂+X₁₃≤40
X₂₁+X₂₂+X₂₃≤90
X₁₁+X₂₁≥30
X₁₂+X₂₂≥40
X₁₃+X₂₃≥60

For (b) eliminate first constraint and label constraints: u₂,v₁,v₂,v₃

Then solve for us and vs and i get u₁=0 u₂=100 v₁=0 v₂=400 and v₃=300

Then c*₁₂=50 so not optimal

(c) Enter X₁₂ into basis create loop etc. but that give new solution as X₁₂=40, X₂₁=30 and X₂₃=60. But then when you go through us and vs again to test for optimality, you've got 5 variables to solve for and only four equations so I'm stuck. Help please!

 

[Ray Vickson]

I don't know if I've posted this in the right place but I thought I'd give it a go anyway.

Homework Statement

See Attatchment

Homework Equations

The Attempt at a Solution

So for part a) max z:150X₁₁+350X₁₂+300X₁₃+100X₂₁+500X₂₂+400X₂₃

s.t. X₁₁+X₁₂+X₁₃≤40
X₂₁+X₂₂+X₂₃≤90
X₁₁+X₂₁≥30
X₁₂+X₂₂≥40
X₁₃+X₂₃≥60

For (b) eliminate first constraint and label constraints: u₂,v₁,v₂,v₃

Then solve for us and vs and i get u₁=0 u₂=100 v₁=0 v₂=400 and v₃=300

Then c*₁₂=50 so not optimal

(c) Enter X₁₂ into basis create loop etc. but that give new solution as X₁₂=40, X₂₁=30 and X₂₃=60. But then when you go through us and vs again to test for optimality, you've got 5 variables to solve for and only four equations so I'm stuck. Help please!

Your new solution is not basic; you need a basis, and since two previously-basic variables were driven to zero simultaneously, you need to drop one and keep the other at level 0; that is, your new basic solution will be degenerate. Either x₁₃ or x₂₂ should drop out of the basis, leaving the other one in at zero value. One of these choices will lead to optimality. Try one, and if it does not work, then try the other.

RGV

 

[tobinator250]

Thanks a lot :)