Problem 1. Write a concrete example of the knapsack problem where you specify a set of at least 5 objects, their dollar values (i.e., benefits) and their weights, as well as the weight of the knapsack, denoted W. Now, consider the greedy approach of sorting items based on decreasing benefit/weight ratios and picking items from the beginning of the list. In the context of your example, show that

Problem 1.a. The greedy approach works for fractional knapsack.

Problem 1.b. The greedy approach may fail for 0-1 knapsack.