Consider the following 0-1 integer programming problem: Minimize 20X + 36Y + 24Z
Subject to: 2X + 4Y + 3Z ≥ 7
12X + 8Y + 10Z ≥ 25
X, Y, Z must be 0 or 1
If we wish to add the constraint that X must be positive, and that only Y or Z, but not both, can be positive, how would the additional constraint(s)be written?
A)X + Y + Z ≤ 3, Y + Z ≤ 1
B)X ≤ 1, Y + Z = 1
C)X ≤ 2, and Y ≤ 2, and Z ≤ 2
D)X = 1, Y + Z ≤ 1

Question

Quizplus · Accepted Answer

The constraint "X must be positive" in a 0-1 integer programming problem means X = 1, since X can only be 0 or 1. The constraint "only Y or Z, but not both, can be positive" translates to Y + Z ≤ 1, ensuring that at most one of Y or Z can be 1 (positive).

Consider the Following 0-1 Integer Programming Problem: Minimize 20X