True or False?

1. We can always solve an integer linear program by rounding down the solution to the linear program after we remove the integrality constraints

2. Let x1, x2, , x5 represent the go vs. no-go decision for five investment options. A requirement of no more than 3 options can be selected simultaneously can be expressed by constraint x1 + x2 + + x5 2.

3. For two minimization problems, P1 and P2. The two problems share the same objective and constraints with the only difference being P2 requires all variables to be integer, while P1 does not. In this case, the optimal objective value for P2 cannot be less than the optimal objective value for P1

4. It is possible for an integer linear program to have more than one optimal solutions