Consider a capital budgeting problem with five projects from which to select. Let us define binary variables x1 = 1 if project 1 is selected, 0 otherwise; x2 = 1 if project 2 is selected, 0 otherwise and so on.

Write the appropriate constraint(s) for each condition a, b, c, d, e and the objective function for part f.

1. Choose no fewer than three projects.
2. If project 3 is chosen, project 4 must be chosen.
3. If project 1 is chosen, project 5 must not be chosen.
4. Projects cost $100, 200, 150, 75, and 300 (in thousands) respectively. The budget is $450,000.
5. No more than two of projects 1, 2, and 3 can be chosen.
6. If the revenues generated by the projects are $400, 100, 265, 80 and 100 (in thousands), write an objective function which maximizes profit.