Consider the following "greedy" strategy for the rod cutting problem: define the density of a rod of length i to be p/i, that is, its value per inch. The greedy strategy for a rod of length n cuts off a first piece of length i, which has the maximum density. It then continues by applying the greedy strategy to the remaining piece of length n - i. a. Write pseudocode for this Greedy strategy for Rod Cutting Problem b. Fill out the density values in the following table Length i (inch) Price (dollar) Density 1 2 a 13. 20 5 21 a 24 c. According to the greedy strategy, if we are to cut a rod of length 6, what is the length of the first piece to cut off? What is the resulting revenue of the greedy solution? Is this the maximum revenue amongst all possible ways of cut (You can represent a way of cut by summation expression, e.g., 6 = 1 + 2 + 3, etc) d. If we are to cut a rod of length 5, what is the solution given by the greedy strategy? (represent it with a summation expression). Does it give the maximum revenue? If not, what is optimal way to cut?