Selection Problem$-$ Homework Question

Suppose that the investment budget is $$14,000.$ We have identified four investment opportunities. Investment $1$ requires an investment of $$5,000$ and has a present value of $$8,000$; investment $2$ requires $$7,000$ and has a value of $$11,000$; investment $3$ requires $$4,000$ and has a value of $$6,000$; and investment $4$ requires $$3,000$ and has a value of $$4,000.$ Additionally, we need to include the following constraints.

$-1.$ We can make at most two investments.

$-2.$ If investment $2$ is made, investment $4$ must also be made.

$-3.$ Investment $1$ and investment $3$ cannot be made together.

Question: Into which investments should we place our money so as to maximize our total present value?