Suppose you work for Amazon Prime delivery services. You are assigned a new town to deliver packages to. You discover that the streets are small enough that you can throw the mail to each persons house on both sides of the street as you drive by. (You may not be the greatest mailman but you sure do finish everything pretty fast!) The photo attached is a representation of all the stops you must make. The locations marked with a red dot are those who have mail that needs to be delivered. You decide to complete all your deliveries as efficiently as possible today. To be most efficient you must drive past each delivery stop only once and you also decide to only drive down roads that have a delivery stop. You must start and end at the exact same spot (that way you can get back to your own car quickly). (i) Is this a possible scenario for a route in which all your wants are met? Describe a route or prove a contradiction. (ii) Unfortunately, as you make your way to the starting point you get a new updated delivery stop (the green dot). Is this a possible scenario for a route in which all your wants are met? Describe a route or prove a contradiction.

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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Suppose you work for Amazon Prime delivery services. You are assigned a new town to deliver packages to. You discover that the streets are small enough that you can throw the mail to each persons house on both sides of the street as you drive by. (You may not be the greatest mailman but you sure do finish everything pretty fast!) The photo attached is a representation of all the stops you must make. The locations marked with a red dot are those who have mail that needs to be delivered. You decide to complete all your deliveries as efficiently as possible today. To be most efficient you must drive past each delivery stop only once and you also decide to only drive down roads that have a delivery stop. You must start and end at the exact same spot (that way you can get back to your own car quickly).
(i) Is this a possible scenario for a route in which all your wants are met? Describe a route or prove a contradiction.
(ii) Unfortunately, as you make your way to the starting point you get a new updated delivery stop (the green dot). Is this a possible scenario for a route in which all your wants are met? Describe a route or prove a contradiction. 
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