$[30$ pts$.]$ Five projects are available for investment. The projects require the cash flows and yield the net present values $($NPV$)($in millions$)$ shown in the following table.

$\backslash$table$[[$Project id$.,$Cash outflow at time $0($million Lira$),$NPV $($million Lira$)],[1,4,2],[2,5,3],[3,3,4],[4,1,1],[5,4,3]]$

If $11$ million Lira is available for investment at time $0,$ find the investment plan that maximizes NPV$.$ All investments are required to be $0$ or $1($fractional investment values are not permitted$).$ Find the optimal solution by using Branch and Bound method $($Draw the branch and bound tree clearly, write also lower bounds$($LB$))($Left branches $x_1=0,$ right branches $x_1=1).$

$-1-$