Consider a capital budgeting problem with six projects represented by \(0-1\ \text{variables}\ x_1,\ x_2,\ x_3,\ x_4,\ x_5,\ \text{and}\ x_6.\)

a. Write a constraint modeling a situation in which two of the projects 1, 3, and 6 must be undertaken.

b. In which situation the constraint "\(x_3\ -\ x_5 = 0\)" is used, explain clearly:

c. Write a constraint modeling a situation in which roject 2 or 4 must be undertaken, but not both.

d. Write constraints modeling a situation where project 1 cannot be undertaken IF projects 3. also is NOT undertaken.

e. Explain clearly the situation in which the following 3 constraints are used simulataneously (together):

\(\displaystyle{x}_{4}\le{x}_{1}\)

\(\displaystyle{x}_{4}\le{x}_{3}\)

\(\displaystyle{x}_{4}\ge{x}_{1}+{x}_{3}-{1}\)