Coin Changing: Suppose we have n denominations {d₁, d₂, ... dn} where each di ≥ 1 is a positive integer. We wish to pay an amount N using the least number of coins possible. We assume that there is an unlimited supply of coins in each denominations. There are two questions in this optimization problem. 1) What is the least number of coins needed to pay N monetary units? There is called the value of an optimal solution 2) Exactly which coins, i. e. how many coins in each denominations are to be disbursed. This is the optimal solution: C[i,j] = the minimum number of coins necessary to pay amount j using only coins in set {d₁,..., d.} 1≤i≤n 0≤j≤N

Coin Changing: Suppose we have n denominations {d₁, d₂, ... dn} where each di ≥ 1 is a positive integer. We wish to pay an amount N using the least number of coins possible. We assume that there is an unlimited supply of coins in each denominations. There are two questions in this optimization problem. 1) What is the least number of coins needed to pay N monetary units? There is called the value of an optimal solution 2) Exactly which coins, i. e. how many coins in each denominations are to be disbursed. This is the optimal solution: C[i,j] = the minimum number of coins necessary to pay amount j using only coins in set {d₁,..., d.} 1≤i≤n 0≤j≤N

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter14: Game Theory

Section14.3: Linear Programming And Zero-sum Games

Problem 5P

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