An air courier company operates a single depot in a large city and wants to decentralize by establishing several depots, each covering the same delivery radius r. We require that the total area covered by all depots is at least 900 square miles. The number of trucks required at each depot is found to be απr3 . Let’s choose α = 0.01 for now. Each truck costs $ 650 per day to operate. Each depot incurs an overhead (fixed) expense of $ 3500 each day. a/ What should the delivery radius r be to minimize cost? What is the minimum cost? b/ What is the optimal number of depots? How many trucks should operate in this case? using modeling and simulation , one variable optimization
An air courier company operates a single depot in a large city and wants to decentralize by establishing several depots, each covering the same delivery radius r. We require that the total area covered by all depots is at least 900 square miles. The number of trucks required at each depot is found to be απr3 . Let’s choose α = 0.01 for now. Each truck costs $ 650 per day to operate. Each depot incurs an overhead (fixed) expense of $ 3500 each day. a/ What should the delivery radius r be to minimize cost? What is the minimum cost? b/ What is the optimal number of depots? How many trucks should operate in this case? using modeling and simulation , one variable optimization
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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Question
An air courier company operates a single depot in a large city and wants
to decentralize by establishing several depots, each covering the same delivery radius r.
We require that the total area covered by all depots is at least 900 square miles. The
number of trucks required at each depot is found to be απr3
. Let’s choose α = 0.01 for
now. Each truck costs $ 650 per day to operate. Each depot incurs an overhead (fixed)
expense of $ 3500 each day.
a/ What should the delivery radius r be to minimize cost? What is the minimum cost?
b/ What is the optimal number of depots? How many trucks should operate in this
case?
using modeling and simulation , one variable optimization
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