Question $2.$ Apply the bottom$-$up dynamic programming algorithm to the following instance of the $\frac{0}{1}-$knapsack problem, with capacity $=6$ and five items with weights: $3,2,1,4,5$ and values: $25,20,15,40,50.$

$\backslash$table$[[$item$,$weight,value$],[1,3,25],[2,2,20],[3,1,15],[4,4,40],[5,5,50]]$

$F(i,j)=$max$\{F(i-1,j),v_i+F(i-1,j-w_i)\}ifj-w_{i}0$

$=F(i-1,j)\{\begin{array}{ccc}\text{:}& if& j-w_{i}0\end{array}$

$F(0,j)=0$ and $F(i,0)=0$