$2.(10$ marks$)$ Use the Backtracking algorithm for the $0-1$ Knapsack problem to maximize the profit for the following problem instance. Show the pruned state space tree produced by using the Backtracking algorithm. Specify the $$profit$,$weight$$ and $$bound$$ from top to bottom at each node in the pruned state space tree $(6$ marks$).$ Mark each nonpromising node with a cross $(2$ marks$).$ Mark the node$($s$)$ with optimal solution $(1$ mark$).$ Mention the value and solution of the problem $(1$ mark$).$ i pi wi $1$ $$2022$ $$3053$ $$357$ W $=94$ $$1235$ $$31$