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Problem 3: Consider the 0,1 knapsack problem defined by max 4x₁ + 3x2 + 2x3 + 3x4 subject to 2x1 + x2 + x3 + x4 <3, x = {0, 1}4. 1. Use the notion of cover to define an equivalent formulation, and discuss whether it is better, worse, or incomparable. 2. Solve the knapsack problem using dynamic programming.

Problem 3: Consider the 0,1 knapsack problem defined by max 4x₁ + 3x2 + 2x3 + 3x4 subject to 2x1 + x2 + x3 + x4 <3, x = {0, 1}4. 1. Use the notion of cover to define an equivalent formulation, and discuss whether it is better, worse, or incomparable. 2. Solve the knapsack problem using dynamic programming.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 3: Consider the 0,1 knapsack problem defined by max 4x₁ + 3x2 + 2x3 + 3x4 subject to 2x₁ + x2 + x3 + x4 ≤ 3, x = {0, 1}4. 1. Use the notion of cover to define an equivalent formulation, and discuss whether it is better, worse, or incomparable. 2. Solve the knapsack problem using dynamic programming.
Transcribed Image Text:Problem 3: Consider the 0,1 knapsack problem defined by max 4x₁ + 3x2 + 2x3 + 3x4 subject to 2x₁ + x2 + x3 + x4 ≤ 3, x = {0, 1}4. 1. Use the notion of cover to define an equivalent formulation, and discuss whether it is better, worse, or incomparable. 2. Solve the knapsack problem using dynamic programming.
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