The Knapsack problem where the objective function is to minimize the profit is

 Answer: D

0/1 Knapsack problem: 

Given a set of n objects which have each have a value v_i and a weight w_i.

The objective of the 0/1 Knapsack problem is to find a subset of objects such that the total value is maximized, and the sum of weights of the objects does not exceed a given threshold W.

An important condition here is that one can either take the entire object or leave it. It is not possible to take a fraction of the object.

Possible Method 1: Look at all possible combinations of objects, calculate their total weight, and if the total weight is less than the threshold, to calculate the total value. This approach is known as the Brute Force. Although this approach would give us the solution, it is of exponential time complexity. Hence, we look at the other possible methods.

Possible Method 2: Use the Dynamic Programming approach to solve this problem. Although this method is far more efficient than the Brute Force method, it does not work in scenarios where the item weights are non-integer values.

Possible Method 3: Backtracking can also be used to solve this problem. By exploring all possible branches until the solution is invalid, then going back a step and exploring other possibilities. This method also has exponential time complexity.

Possible Method 4: Since this is a combinatorial problem, once can use the Branch and Bound method to solve this problem. Thing to be noted is that the Branch and Bound method is for minimization problems.