# Constraints of an L-shaped feasible region

1. Oct 12, 2014

### Jimbrisky

I am writing the constraints for the feasible region within the L-shaped feasible region. The diagram is at this link.

Are these equations the right constraints:

–1 ≤ x ≤ 1 and 0 ≤ y ≤ 1

Thanks for the help.

2. Oct 12, 2014

### Staff: Mentor

No. These inequalities give you the rectangle whose corners are at (-1, 1), (1, 1), (1, 0), and (-1, 0). To get the whole L-shaped region you also need these constraints: 0 ≤ x ≤ 1 and -1 ≤ y ≤ 0.

The diagram at the page you linked to says this (slightly changed to use your x, y notation):

A point is in the rectangle –1 ≤ x ≤ 1 and 0 ≤ y ≤ 1 OR a point is in the rectangle 0 ≤ x ≤ 1 and -1 ≤ y ≤ 0

3. Oct 12, 2014

### Jimbrisky

@Mark44, based on your explanation can I write the constraints for the feasible region as the union of two sets, Rx∪Ry, where

Rx:={(x,y):−1≤x≤1,0≤y≤1}

Ry:={(x,y):0≤x≤1,−1≤y≤1}.

Thanks for the help.

4. Oct 12, 2014

### Staff: Mentor

Yes, although I don't know why you call one set Rx and the other one Ry. Better names might be R1 and R2.