Consider a capital budgeting problem with five projects from which to select. Let us define binary variables -1 if project 1 is selected, O otherwise; X2 : 1 if project 2 is selected, 0 otherwise and so on. o otherwise and lo on binary Write the appropriate constraint(s) for each condition a, b, c, d, e and the objective function for part f a. Choose no fewer than three projects. b. If project 3 is chosen, project 4 must be chosen. c. If project 1 is chosen, project 5 must not be chosen. d. Projects cost $100, 200, 150, 75, and 300 (in thousands) respectively. The budget is $450,000 e. No more than two of projects 1, 2, and 3 can be chosen. f. If the revenues generated by the projects are $400, 100, 265, 80 and 100 (in thousands), write an objective function which maximizes profit