Example $1$: Capital Budgeting Problem

The following questions refer to a capital budgeting problem with six projects represented by binary

variables x$1,$ x $2,$ x$3,$ x$4,$ x $5,$ and x$6.$

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 $3$

also are undertaken.

e$.$ Revise the requirement in part d to accommodate the case in which, when project $1$ or $3$ is

undertaken, project $4$ also must be undertaken.

f$.$ Revise the requirement in part d to accommodate the case in which, when projects $1$ and $3$ are

undertaken, project $4$ also must be undertaken.