Five projects are avalatis to invent The propta agine ta cat lon ve yesthe net present values $($NP$)$ in miions shown in te toicking beleProject id$1,11$ million Lira is available for investment al tre O$,$ find tre nester den ra taircan $2$t All investments are required to be $0$ or $1($trasional metret rela re no eate esta optimal solution by using Branch and Bound method Dran tre trach and toad te o write also lower bounds LB$)($Left branches x$=0,$ nght oracten salyFive projects are available for investment. The projects require the cash flows and yield the net present values $($NP$)($in millions$)$ shown in the following table.

$\backslash$table$[[$Project id$.,$Cash ourflow at time O $($million Lira$),$NfV $($million Lira$)],[1,4,2],[2,5,3],[3,3,4],[4,1,1],[5,4,3]]$

If $11$ million Jira is available for investment at time $0,$ find the investment plan that maximizes NPV$.$ All investments are required to be $0$ or $1($fractronal investment values are not permitled$).$ Find the optimal solution by using Bronch and Bound method. $($Draw the branch and bound tree clearly.

Write also lower bounds $($LB$).($Left bronches $x=0,$ right bronches $x=1)$