Consider a capital budgeting example with five projects from which to select. Let Xi = 1 if project i is selected, 0 if not, for i = 1,2,3,4,5.

Projects cost are $100, $200, $150, $75, and $300, respectively. Suppose that the budget is $450.

Consider the following requirements:

1. Choose at least 3 projects,

2. If project 3 is chosen, project 4 must not be chosen, and

3. the total cost cannot exceed the budget

4. projects 4 and 5 cannot be both selected