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

hi your question is in complete here is the complete question

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

Answer : at least 2 , 4 ( D )

Explanation:

Given xj = 1

if project j is selected and xj = o

using the 0-1 integer programming, 0-1 variable provide selection with the value of a variable equal to 1 when another activity is selected and equal to zero if the corresponding activity is not selected .

x1 = 0 or 1 , x2 = 0 or 1 , x3 = 0 or 1 , x4 = 0 or 1

for the summation of the four projects to be 2, at least any of the two out of the four projects must be selected and summed up

hence my answer of at least 2 out of 4