# Homework Help: Big m method / two-phase method

1. Feb 20, 2012

### csc2iffy

1. The problem statement, all variables and given/known data
Minimize Z = 3.5x + 6.5y
subject to
1. (1/3)x + y ≥ 1
2. 3.8x + 2.4y ≥ 5
and x ≥ 0, y ≥ 0

Use Big M method and then Two-Phase method interactively with IOR.jar and compare answers.

2. Relevant equations

3. The attempt at a solution
I am getting really confused with IOR, but this is what I have

Big M Method:

Minimize Z = 3.5x + 6.5y + Ma + Mb --> Max(-Z) = -3.5x - 6.5y - Ma - Mb -->
-Z + 3.5x + 6.5y + Ma + Mb = 0
subject to
1. (1/3)x + y - u + a = 1
2. 3.8x + 2.4y - v + b = 5
and x, y, u, v, a, b ≥ 0

I attached my IOR txt file... just wondering if it's all right?
Not sure how to do the Two-Phase method on iOR, there isn't an example in the book.. help please?

#### Attached Files:

• ###### big m method.txt
File size:
1.5 KB
Views:
106
2. Feb 20, 2012

### Ray Vickson

The two-phase method starts by trying to get a basic feasible solution (or prove infeasibility). It does this by first solving the problem min (a + b), subject to the constraints you wrote for the Big M problem.

RGV