a$.$ Apply the dynamic programming algorithm to the following instance of the $0-1$ knapsack problem:

$\backslash$table$[[$Item$,$Weight,Value$],[1,3,30],[2,2,20],[3,1,15],[4,4,40],[5,5,45]]$

$\backslash$table with capacity $W=7.$ Show your pseudo codes for the dynamic programming solution. You should include a procedure to retrieve an optimal solution.

b$.$ How many different optimal subsets does the instance of part $($a$)$ have? Show all optimal subsets.

c$.$ In general, how can we use the table generated by the dynamic programming algorithm to tell whether there is more than one optimal subset for the knapsack problem's instance?