Consider the following 0 - 1 integer programming problem: 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
E)None of the above

Question

Consider the following 0 - 1 integer programming problem:  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 
E)None of the above

Quizplus · Accepted Answer

To ensure that X is positive, we can add the constraint X ≥ 1. To ensure that only Y or Z can be positive, we can add the constraint Y + Z ≤ 1. Therefore, the correct choice is D: X = 1, Y + Z ≤ 1.

Consider the Following 0 - 1 Integer Programming Problem