Problem $3(20$ points$)$

Let $v_t(s_t)be$ the maximum benefit that can $be$ carned for item $t$ given $an{s}_t-$pound knapsack

assuming the optimal policy $is$ followed for stage $t$ and all future stages. Suppose the knapsack

has a capacity $of101l$ and $istobe$ filled with the following items:

Item $1$: $3lbs,$ Bencfit $7$

Item $2$: $4lbs,$ Benefit $11$

Item $3$: $5lbs,$ Benefit $12$

Find the optimal items $to$ select $in$ the knapsack $to$ maximize the total benefit.