Suppose you are the manager of a company that manufactures metal rods of variable lengths. You have a rod of length L, and you want to cut it into smaller rods of lengths 1, 2, ..., L (That is, the cut pieces of rods always have integral length). Each rod of length i has a certain price vi in the market. In the rod cutting problem, you are supposed to determine the maximum revenue that can be obtained by cutting up the rod into pieces of integral length and selling them in the market. Now write a paper that discusses the rod-cutting problem, and how it can be solved by using dynamic programming. Your paper should include the following: 1. A description of the rod-cutting problem, including a clear definition of the input and output 2. An overview of the dynamic programming approach to solving the rod cutting problem, including a description of the subproblems, the recurrence relation and the base cases 3. A pseudocode or step-by-step explanation of a program that implements the dynamic programming approach 4. A detailed example problem in which you are using the program to solve the rod-cutting problem 5. A discussion of the time and space complexity of the dynamic programming solution