Consider the Knapsack problem solved by the Dynamic Programming. Consider the following weights: w$1=2,$ w$2=1,$ w$3=3,$ w$4=2$ and the corresponding values of v$1=3,$ v$2=1,$ v$3=2,$ v$4=4,$ with maximum knapsack capacity of W $=5.$ Let F$($i$,$ j$)$ be the value of the most valuable subset of the first i items that fits in the knapsack of capacity j$.$ How is F$(2,4)$ evaluate?

Question $9$ options:

F$(2,4)=$ max $\{$ F$(4,1),$ F$(3,1)+2\}$

F$(2,4)=$ F$(1,4)$

F$(2,4)=$ max $\{$ F$(1,4),$ F$(1,3)+1\}$

F$(2,4)=$ F$(1,3)+1$