Apply the bottom$-$up dynamic programming algorithm to the following instance of the $0-1$ knapsack problem. Also, show how you compute which items are in the

optimal set. Show all of your work.

item $[1,2,3,4,5]$

weight $[3,2,5,1,4]$

value $[8,7,16,4,15]$

Capacity W $=8$