2. The following questions refer to a capital budgeting problem with six project

Question

2. The following questions refer to a capital budgeting problem with six projects represented by binary variables a, b, c, d, e, and f.

a. Write a constraint modeling a situation in which two of the projects 1, 3, 5, and 6 must be undertaken.

b. Write a constraint modeling a situation in which, if project 3 or 5 is undertaken, they must both be undertaken.

c. Write a constraint modeling a situation in which project 1 or 4 must be undertaken, but not both.

d. Write constraints modeling a situation where project 4 cannot be undertaken unless projects 1 and 3 are also undertaken.

e. Revise the requirement in part (d) to accommodate the case in which, when projects 1 and 3 are undertaken, project 4 must also be undertaken.

Explanation / Answer

In case of binary variables, 1 is when we decide to undertake the project and 0 stands when the project is to be rejected.
a - Project 1
b - Project 2
c - Project 3
d - Project 4
e - Project 5
f - Project 6

1. Write a constraint modeling a situation in which two of the projects 1, 3, 5, and 6 must be undertaken.
a + c + e + f = 2

2. Write a constraint modeling a situation in which, if project 3 or 5 is undertaken, they must both be undertaken.
c - e = 0

3. Write a constraint modeling a situation in which project 1 or 4 must be undertaken, but not both.
a + d = 1

4. Write constraints modeling a situation where project 4 cannot be undertaken unless projects 1 and 3 are also undertaken.
d < a
d < c

5. Revise the requirement in part (d) to accommodate the case in which, when projects 1 and 3 are undertaken, project 4 must also be undertaken.
d < a
d < c
d > a + c - 1

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