You are given a knapsack with capacity T$=7$ and the following three items:

$($Item $1)$ weight w$(1)=5,$ value v$(1)=6$

$($Item $2)$ weight w$(2)=4,$ value v$(2)=4$

$($Item $3)$ weight w$(3)=2,$ value v$(3)=3$

Let OPT$($i$,$U$)$ be the value of the optimal solution to the knapsack problem with items chosen from $\{1,...,$ i$\},$ and a knapsack capacity of U$.$ For the next set of questions you will have to compute some of the values OPT$($i$,$U$).$

Question $1$:

What is OPT$(0,7)?$

Question $2$:

What is OPT$(3,6)?$

Question $3$:

What is OPT$(2,3)?$