$\backslash$#$7$ The knapsack problem was covered in class lecture. Below is a set of $5$ items, each with a weight and value. Create the table to solve the maximum value and the items you would take given a weight constraint of $6.$

$($a$)$ I created the table, F$,$ you will "run" the algorithm and fill in every blank cell.

$($b$)$ The solution to the problem is in which cell?

$($c$)$ If the problem only allowed items $1-4$ with a weight constraint of $5,$ what is the maximum total value?

$($d$)$ Decode the table and determine which items you will take to achieve the maximum total value.