Consider a capital budgeting example with 5 projects from
which to select. Let x1 = 1 if project a is selected, 0 if not, for a = 1, 2,
3, 4, 5. Projects cost $100, $200, $150, $75, and $300 respectively. The budget
is $450. Write the appropriate constraint for the following conditions:

Choose no fewer than 3 projects.

If project 3 is chosen, project 4 must be chosen.

If project 1 is chosen, project 5 must not be chosen.

Write the appropriate constraints for the budget constraint.

No more than 2 of projects 1, 2, and 3 can be chosen.