1.5 Problem 5 [20 pts]
Problem 5. Consider the following input for the Knapsack problem with a capacity W = 12:
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
item $i$ & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
value $v_i$ & 2 & 7 & 18 & 23 & 29 & 35 \\
weight $w_i$ & 1 & 2 & 5 & 6 & 7 & 9 \\
\hline
\end{tabular}
Fill in a lookup table, similar to the example on page 12 of course notes for week 8 (see Week 8 under \"Modules\"
of the course canvas). In addition, clearly explain how you obtain the maximum values/profits $OPT(6, w)$,
$w = 7, 8, 9, 10, 11, 12.$
Answer.