Q$2)(25$ pts$)$ Four projects are available for investment. The projects require the cash flows $($investment$)$ and yield the net present values $($NPV$)($in millions$)$ shown in the table below. If $\backslash (\backslash$$ $12\backslash )$ million is available for investment at time $0,$ find the investment plan that maximizes NPV$.$

a$)$ Formulate the problem as a knapsack problem

b$)$ Solve the model using the branch and bound procedure designed for knapsack problems. Note that each subproblem must be solved by hand.