I think it is best learned by example, so we will mostly do examples today. CLRS Exercise 15.1-3 Rod Cutting Problem with cost My Macroeconomics class starts to talk about dynamic optimization this week, so I think it might be a good idea for me to jump ahead to work on some dynamic programming problems in CLRS books. Write a recursive method named rodCutting that solves the classic "rod cutting" problem using backtracking. Question: In The Rod-cutting Problem, Assume That Each Cut Costs A Constant Value C. As A Result, The Revenue Is Now Calculated As The Total Prices Of All Pieces Minus The Cost Of The Cuts. Top Down Code for Rod Cutting. Section The Bin Packing Problem presents a straightforward formulation for the bin packing problem. Imagine a factory that produces 10 foot (30 cm) lengths of rod which may be cut into shorter lengths that are then sold. Perhaps more popular lengths command a higher price per foot. This chapter is structured as follows. Cutting-stock problems can be classified in several ways. Objective: Given a rod of length n inches and a table of prices p i, i=1,2,…,n, write an algorithm to find the maximum revenue r n obtainable by cutting up the rod and selling the pieces. One way is the dimensionality of the cutting: the above example illustrates a one-dimensional (1D) problem; other industrial applications of 1D occur when cutting pipes, cables, and steel bars. The lengths are always a whole number of feet, from one foot to ten. Two-dimensional (2D) problems are encountered in furniture, clothing and glass production. Like given length: 100, cutting number : 3 , and it will cut at 25, 50, 75. If u cut at 50 it cost 100, and then cut at 25 it cost 50, last cut at 75 cost 50. and it'll give back least money cost: 200 Let's look at the top-down dynamic programming code first. As the problems are equivalent, deciding which to solve depends on the situation. Naive solution: Rod cutting problem. Dynamic programming is a problem solving method that is applicable to many di erent types of problems. Code for Rod cutting problem. Rod Cutting Input: We are given a rod of length n and a table of prices p i for i = 1;:::;n; p i is the price of a rod of length i. The demand for the different lengths varies and so does the price. The Rod Cutting Problem. (a) Update The Equation Below That Computes The Optimal Revenue To Include The Cutting Costs: In = Max (Pi + In-i). 1 Rod cutting Suppose you have a rod of length n, and you want to cut up the rod and sell the pieces in a way that maximizes the total amount of money you get. The idea is that you are given a rod that can be cut into pieces of various sizes and sold, where each piece fetches a given price in return, and you are trying to find the optimal way to cut the rod to generate the greatest total price. 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