Assume that we are using 01 integer programming model to sol

Assume that we are using 0-1 integer programming model to solve a capital budgeting problem and xj = 1 if project j is selected and xj = 0, otherwise. The constraint (x1 + x2 + x3 + x4 = 2) means that ________ out of the ________ projects must be selected.

A. at most 1, 2

B. exactly 1, 2

C. exactly 2, 4

D. at least 2, 4

Solution

Given xj=1 if project j is selected and xj=0, otherwise.

The given constraint is x1+x2+x3+x4=2

where x1, x2, x3 and x4 are 4 projects.

To satisfy the given constraint any two out of 4 projects must be selected.

If we select 3 projects out of 4 than x1+x2+x3+x4 will equal 3. Which will not satisfy the given constraint.

Hence exactly 2 projects out of 4 projects must be selected.