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Constraints of an L-shaped feasible region

  1. Oct 12, 2014 #1
    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. jcsd
  3. Oct 12, 2014 #2

    Mark44

    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
     
  4. Oct 12, 2014 #3
    @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.
     
  5. Oct 12, 2014 #4

    Mark44

    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.
     
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