Given the following knapsack problem:

item $$ weight$$ value$$ Knapsack capacity W$=12$

$12$ lbs$$ $$40$

$25$ lbs$$ $$65$

$36$ lbs$$ $$72$

$44$ lbs$$ $$60$

Find the most valuable subset of the items that fit into the knapsack. You must show and explain your intermediate steps for the following questions.

a$)$ If it is a fractional knapsack problem, provide the optimal solution using greedy algorithm $($Greedy strategy: choosing items with greatest value per pound$)$