Xcellenta Systems is a local software development firm that is currently evaluating six different

potential projects. There are not sufficient resources to take on all of these, but more than one

will be selected. A $0-1$ integer programming model is planned to help determine which of the

six opportunities to choose, and variables X$1,$ X$2,$ X$3,$ X$4,$ X$5,$ and X$6$ are being used to represent

the six choices. For each of the following situations, please write a constraint $($or several

constraints$)$ that would accomplish the stated restriction:

$($a$)$ At least $3$ of these choices are to be selected

$($b$)$ Either project $1$ or project $4$ must be undertaken, but not both

$($c$)$ If project $4$ is selected, then project $6$ must also be selected. However, if project $4$ is

not selected, it is still possible to select project $6.$

$($d$)$ Project $5$ cannot be selected unless both projects $2$ and $3$ are also selected.

$($e$)$ Project $5$ must be selected if both projects $2$ and $3$ are also selected.