Consider a budget allocation problem where $$58$ million is available for a number of projects listed below. The investment required in each project along with the expected return in terms of utility is also given. The problem is to find which projects should be financed in order to maximize the total expected utility not exceeding the budget limitation$.$ Now suppose there are additional conditions in selecting the projects. Write the constraints for these conditions.

Any three of the five projects must be undertaken.

Projects $1$ and $3$ must be taken simultaneously or not taken at all.

$•$ Project$-1$ will be undertaken only if project$-3$ is undertaken but project$-3$ is not conditional on project$-$l $($that means, you can have project$-3$ without project$-1,$ but you cannot have project$-$l unless project$-3$ is undertaken$).$