Q$3(25$ pts$)$ The table$/$matrix below shows the profit $($in millions of dollars$)$ obtained by allocating $,1,2,3,4$ units of a resource to four different projects $(1,2,3,4).$ Determine the optimal allocation of the units of the resources to the projects such that the total profit obtained across all the projects is the maximum. Use the multi$-$stage graph largest weight path approach. Show all the work.

Profit Matrix Resource

$\backslash$table$[[\backslash$table$[[$Project$],[1]],0,1,2,3,4],[0,1,4,5,7],[2,0,2,5,6,9],[3,0,1,3,4,6],[4,0,2,4,6,8]]$