Formulating an LP problem (Mathematics/Engineering)

[bobbo7410]

Homework Statement

I don't exactly have a specific example, I'm looking for the general idea behind LP constraints.

Homework Equations

Within the constraints, do the variables have to be all to one side?

For instance, X1 + 2 > 3 is a standard constraint

would for example

X1 + 2 > X1 + 1

still be acceptable as a constraint?

 

[Mark44]

Homework Statement

I don't exactly have a specific example, I'm looking for the general idea behind LP constraints.

Homework Equations

Within the constraints, do the variables have to be all to one side?

For instance, X1 + 2 > 3 is a standard constraint

This would normally be written as x₁ > 1. Did you mean x₁ + 2x₂ > 3?

would for example

X1 + 2 > X1 + 1

still be acceptable as a constraint?

No. This is equivalent to 2 > 1, which is always true, so doesn't constrain things in any way. Did you mean x₁ + 2 > x₂ + 1?

That could be written as x₁ - x₂ > -1

 

[bobbo7410]

I'm sorry, it was late and my examples are horrible. They do not confine to standard constraints, they were simply just numbers to illustrate.

The basic question is, can you have variables on both sides of a constraint? Or must the variables be confined to one side?

 

[Mark44]

You can always move variables from one side of an equation/inequality to the other.

 

[bobbo7410]

You can always move variables from one side of an equation/inequality to the other.

Yes I understand that, my question is, must I?

I recently took a test, and after looking through the examples, they set the constraints equal to 0 and isolated all the variables to one side. I left the constraints with variables on both sides. Not sure if I would get points off for doing so...

 

[Mark44]

To use matrix methods (e.g., Simplex tableau), you need to have all the variables on one side, and the constant on the other. I'm pretty sure this is correct, although I haven't done one of these problems for a good long while.

 

[bobbo7410]

To use matrix methods (e.g., Simplex tableau), you need to have all the variables on one side, and the constant on the other. I'm pretty sure this is correct, although I haven't done one of these problems for a good long while.

Gotcha yeah, that makes sense. I suppose it wouldn't be completely incorrect, yet not properly done. Anyway I'll find out soon enough.

Thanks for your help!