In formulating a mixed integer programming problem, the constraint x1 + x2 ≤ 500y1 where y1 is a 0-1 variable and x1 and x2 are continuous variables, then x1 + x2 = 500 if y1 is ________.
A) 0
B) 1
C) 0 or 1
D) none of the above

Question

Quizplus · Accepted Answer

If y1 is 1, then x1 + x2 ≤ 500 but x1 + x2 must also be maximized; this occurs when x1 = x2 = 250. Therefore, x1 + x2 = 500. If y1 is 0, then the constraint becomes x1 + x2 ≤ 0, which is not feasible. Therefore, the only option that satisfies x1 + x2 = 500 is when y1 is 1.

In Formulating a Mixed Integer Programming Problem, the Constraint X1