Consider a budget allocation problem where $30 million is available for a number of projects listed...
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Consider a budget allocation problem where $30 million is available for a number of projects listed below. The investment required in each project along with the expected return in terms of utility is also given. Project Number 1 2 3 4 5 Project After-school program Road security Crime reduction Road extension Child care facility Cost ($ million) 6 18 10 9 4 Expected Utility 18 16 12 25 14 (a) The problem is to find which projects should be financed in order to maximize the total expected utility not exceeding the budget limitation. Formulate the problem in integer programming. (b) Now suppose there are additional conditions in selecting the projects. Write the constraints for these conditions. • Any two of the first four projects must be undertaken. • Projects 1 and 3 must be taken simultaneously or not taken at all. • Project-1 will be undertaken only if project-3 is undertaken but project-3 is not conditional on project-1 (that means, you can have project-3 without project-1, but you cannot have project-1 unless project-3 is undertaken). Consider a budget allocation problem where $30 million is available for a number of projects listed below. The investment required in each project along with the expected return in terms of utility is also given. Project Number 1 2 3 4 5 Project After-school program Road security Crime reduction Road extension Child care facility Cost ($ million) 6 18 10 9 4 Expected Utility 18 16 12 25 14 (a) The problem is to find which projects should be financed in order to maximize the total expected utility not exceeding the budget limitation. Formulate the problem in integer programming. (b) Now suppose there are additional conditions in selecting the projects. Write the constraints for these conditions. • Any two of the first four projects must be undertaken. • Projects 1 and 3 must be taken simultaneously or not taken at all. • Project-1 will be undertaken only if project-3 is undertaken but project-3 is not conditional on project-1 (that means, you can have project-3 without project-1, but you cannot have project-1 unless project-3 is undertaken).
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a The integer programming formulation is Maximize 18x1 16x2 12x3 25x4 14x5 Subjec... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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