1. Suppose we have a knapsack that can hold at most 7 pounds. The table below lists the weight and value of four items. Assume we can pack fractions of the items. Use a greedy algorithm to solve this fractional knapsack problem (i.e., maximizing the total value of packed items). Show your work. item weight value 1 2 pounds $3.00 2 3 pounds $2.00 3 4 pounds $4.00 4 5 pounds $1.00 2. Consider a special case of the 0-1 knapsack problem in which the order of the items sorted by increasing weight is the same as their order when sorted by decreasing value. Give an efficient algorithm to find an optimal solution (for this special case) that maximizes the value of the packed items. And argue that your algorithm is correct.

1. Suppose we have a knapsack that can hold at most 7 pounds. The table below lists the weight and value of four items. Assume we can pack fractions of the items. Use a greedy algorithm to solve this fractional knapsack problem (i.e., maximizing the total value of packed items). Show your work. item weight value 1 2 pounds $3.00 2 3 pounds $2.00 3 4 pounds $4.00 4 5 pounds $1.00 2. Consider a special case of the 0-1 knapsack problem in which the order of the items sorted by increasing weight is the same as their order when sorted by decreasing value. Give an efficient algorithm to find an optimal solution (for this special case) that maximizes the value of the packed items. And argue that your algorithm is correct.