Consider a capital budgeting example with five projects from which to select. Let xi $=1$ if project i is selected, $0$ if not, for i $=1,...,5.$ Write the appropriate constraint$($s$)$ for each condition. Conditions are independent. $($a$)$ Choose no fewer than four projects.

$($b$)$ If project $1$ is chosen, project $5$ must be chosen.

$($c$)$ If project $3$ is chosen, project $4$ must not be chosen.

$($d$)$ Projects cost $100,200,150,75,$ and $300,$ respectively. The budget is $450.$

$($e$)$ No more than two of projects $2,3,$ and $4$ can be chosen.