Fixed-requirement constraints in a linear programming model are functional constraints that use an equal sign. O True O False

Knapsack 0/1 problem: Given N items where each item has some weight and profit associated with it and also given a bag with capacity W, [i.e., the bag can hold at most W weight in it]. The task is to put the items into the bag such that the sum of profits associated with them is the maximum possible. Given the problem is solved using a dynamic programming approach and the matrix derived is given below, answer the below set of questions by analyzing the DP matrix. weights = [2, 3, 4, 5], profits = [1, 2, 5, 6], Capacity W = 8 Capacity 2 3 Profits weights|0 1 2 5 16 14 |-> 5 10 0 O 10 1 2 3 4 0 O 0 1 1 0 1 0 1 O 10 1 2 2 2 5 2 O 15 50 1 356 6 O 1 3 6 18 00378 7 10 10 1 3 7 7 1 18

Q1 Dan has a list of problems suitable for the assignment. The difficulties of these problems are stored in a list of integers a. The i-th problem’s difficulty is represented by a[i] (the higher the integer, the more difficult the problem). Dan is too busy eating saltines to worry about assignment decisions, so he asks Michael to select at least two problems from the list for the assignment. Since there are many possible subsets of the problems to consider and Michael has a life, he decides to consider only sublists (definition follows) of the list of problems. To make grading the assignment easier, Michael wants to pick problems that don’t vary too much in difficulty. What is the smallest difference between the difficulties of the most difficult selected problem and the least difficult selected problem he can achieve by selecting a sublist of length at least 2 of the original list of problems? Definition: A sublist of a list a is any list you can obtain by removing some (possibly 0)…

Rod cutting problem: A cutting factory buys long steel rods and then and cuts them into shorter rods, which it then sells. Each cut is free. The selling price is based on the length of the cut. The factory want to determine the best cuts in order to maximize its revenue. Below, the price that the factory can make for each length of rod is given. Determine the maximum revenue, rn, obtainable by cutting up the rod and selling the pieces using bottom-up dynamic-programming approach. Length, I 1 2 3 4 5 6 7 Price, pi 2 4 5 6 9 10 12   r5 = ?