Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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a. Given n items, where each item has a weight and a value, and a knapsack that can carry at most W You are expected to fill in the knapsack with a subset of items in order to maximize the total value without exceeding the weight limit. For instance, if n = 6 and items = {(A, 10, 40), (B, 50, 30), (C, 40, 80), (D, 20, 60), (E, 40, 10), (F, 10, 60)} where each entry is represented as (itemIdi, weighti, valuei). Use greedy algorithm to solve the fractional knapsack problem.
b. Given an array of n numbers, write a java or python program to find the k largest numbers using a comparison-based algorithm. We are not interested in the relative order of the k numbers and assuming that (i) k is a small constant (e.g., k = 5) independent of n, and (ii) k is a constant fraction of n (e.g., k = n/4). Provide the Big-Oh characterization of your algorithm.
Solve the 0/1 Knapsack problem given that:
The Knapsack can only carry a maximum of 8 Kg. The items are 2 Kg with a value of Ksh 100, 3 Kg with a value of Ksh 120, 5 Kg with a a value of Ksh 140, 1 Kg with a value of Ksh 60, and 6 Kg with a value of Ksh 150.
Given a symmetric propagationmatrix W and the general initial condition c^0' = 0 or Ai = 0. If option x*(x* G Di) is in the global optimum, then c\ {x*) must satisfy the followinginequality,^«)<f+y^i4 k ) i ^ .
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