Consider the following knapsack problem with extra constraints: The tourism depa
ID: 439864 • Letter: C
Question
Consider the following knapsack problem with extra constraints: The tourism department of a certain country would like to decide which projects to fund during the coming year. The projects were divided into three main categories: 1. Religious, 2. Historical, and 3. Construction. There are project proposals (labeled A{L) submitted with associated scores (value) and costs in each category, as summarized in the table below: Religious Historical Construction Projects: A B C D E F G H I J K L Score 5 6 2 8 11 l 7 2 10 9 5 4 Cost ($million) 5 7 3 15 12 5 7 2 15 22 8 10 A bigger score has more value. The tourism department decides that at least one project of each category must be funded. Projects E and F represent a continuation of a plan that started during the previous year, and at least one of them must be funded. Furthermore, at most two historical and three construction projects can be chosen. Which projects should the tourism department fund in order to maximize the total score and not to exceed $80 million budget? Formulate a mathematical model.Explanation / Answer
Consider the following knapsack problem with extra constraints: The tourism department of a certain country would like to decide which projects to fund during the coming year. The projects were divided into three main categories: 1. Religious, 2. Historical, and 3. Construction. There are project proposals (labeled A{L) submitted with associated scores (value) and costs in each category, as summarized in the table below: Religious Historical Construction Projects: A B C D E F G H I J K L Score 5 6 2 8 11 l 7 2 10 9 5 4 Cost ($million) 5 7 3 15 12 5 7 2 15 22 8 10 A bigger score has more value. The tourism department decides that at least one project of each category must be funded. Projects E and F represent a continuation of a plan that started during the previous year, and at least one of them must be funded. Furthermore, at most two historical and three construction projects can be chosen. Which projects should the tourism department fund in order to maximize the total score and not to exceed $80 million budget? Formulate a mathematical model.
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