Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Chapter 9, Problem 33RP
Program Plan Intro
To determine:
The beam that should be used to maximize the amount of radiation.
Introduction:
The variation between the present value of the cash outflows and the present value of the cash inflows are known as the Net Present Value (NPV).
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John is training for a marathon and he can easily alternate between running a mile and walking a mile. If he runs for 2 miles in a row, he becomes fatigued, and must then walk for 2 miles in a row in order to no longer be fatigued. When he is fatigued, he can still alternate between running a mile and walking a mile, but if he runs 2 miles in a row while already fatigued, he will collapse on the side of the road. If he runs 3 miles in a row at any point, he will also collapse. Let the letter 'a' stand for John running 1 mile, and the letter 'b' stand for John walking 1 mile. Draw a DFA which accepts all possible runs in which John does not collapse on the side of the road.
With this exercise, we shall develop a solution to the following riddle.
Two adults, their three children, and their dog are on a walk when they come upon a river. They have a boat, but it can only hold a maximum of one adult with either one child or the dog; or three chidren; or two children and the dog. Anyone (other than the dog) can row the boat; but it would be too much work for one child to row across by themself. How can they all get across the river? You are required to solve this riddle by modelling it using a labelled transition system (LTS).
1. What are the states of your LTS consist of? Make sure you consider all the aspects of the riddle. Justify your notion of state.
2. What are the actions of your LTS? List all the actions. Justify your choice of actions.
3. Drawing out the entire LTS may be a time consuming task as there could be very many states and transitions. However, drawing out only part of the LTS is doable. Draw part of the LTS, anywhere between 7 and 12…
Recall Pigou’s example discussed in class, where there are two roads that connect a source, s, and destination, t. The roads have different travel costs. Fraction x1 of the traffic flow on route 1, and the remainder x2 on route 2. Here consider the following scenario. • The first road has “infinite” capacity but is slow and requires 1 hour travel time, T1 = 1. • The second road always requires at least 15 mins, which then increases as a function of traffic density, T2 = 0.25 + 0.75x2. If drivers act in a “selfish” manner – the user optimal scenario – all the traffic will flow on the second path, as one is never worse off. Worst case scenario for path 2, both paths take one hour. So no one is incentivized to change their behavior. 1. Assume user optimal behavior, and calculate τ the expected travel time per car. 2. If instead we could control the flows, we could minimize the expected travel time. Using the expression in part (a), calculate the optimal allocation of flows x¯1 and ¯x2…
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Operations Research : Applications and Algorithms
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Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
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