You have been asked to recommend which projects should be funded. Given the annual budget, your goal is to determine which projects to invest in to maximize the overall NPV$.$ Please note that:

$1)$ Aprojectcanbeeitherfullyfundedornotfunded,butnotpartiallyfunded. $2)$ Capitalthatisnotusedinthecurrentyearcannotbecarriedovertothenext

year.

Please provide the algebraic model of your formulation. Clearly define your decision variables, objective function, and constraints.

Suppose the CEO says, $$At least two of the projects $1,2,$ and $4$ must be undertaken.$$ Describe the constraint.

Suppose the CEO says, $$Either Project $3$ or Project $4$ must be undertaken, but not both.$$ Describe the constraint.

Suppose the CEO says, $$Project $5$ is undertaken only if at least one of Projects $3$ and $6$ is also undertaken.$$ Describe the constraint.