particular, we assume that the transportation network is given by a set A of arcs, where (i, j) ∈ A means that there exists a route connecting the provider i and the demander j. We denote by cij the unit shipment cost on the arc (i, j), by si the available supply at the provider i , and by dj the demand at the demander j. The variables are the quantities xij of the commodity that is shipped over the arc (i, j) ∈ A and the problem is to minimize the transportation costs (1.1) minimize (i,j)∈A cij
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Generalization: A generalization of this problem as well as its preceding problem (When is Cheryl’s Birthday) would be to connect these questions to the ideas of the birthday paradox, and an even bigger idea of the pigeonhole principle. In math, the pigeonhole principle states that if there are n items to be put into m containers, with the criteria that n > m, then at least one container will hold more than one item. (Herstein, 1964) Another way to explain this principle in a more quantitative
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Ms. Pierce/Mr. Gross 23 March 2011 Lighting: The Way it Affects a Movie Set Lights! Lights! And More Lights! While on a movie set for any show, cinematographers are artists that paint motion pictures with light (Murphy 1). They must know that lighting is their main concern while in production. No matter if there is too much or too little lighting, lighting must always be controlled (Morales). In order to solve the problem of faulty lighting, cinematographers should know when lights should be used
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Natural Computing Series Series Editors: G. Rozenberg Th. Bäck A.E. Eiben J.N. Kok H.P. Spaink Leiden Center for Natural Computing Advisory Board: S. Amari G. Brassard K.A. De Jong C.C.A.M. Gielen T. Head L. Kari L. Landweber T. Martinetz Z. Michalewicz M.C. Mozer E. Oja G. P˘ un J. Reif H. Rubin A. Salomaa M. Schoenauer H.-P. Schwefel C. Torras a D. Whitley E. Winfree J.M. Zurada For further volumes: www.springer.com/series/4190 Franz Rothlauf Design of Modern Heuristics Principles
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were required to perform Change the switch hostname to Branch1 Add a description to FastEthernet 0/1 Add a description to FastEthernet 0/2 Add a description to FastEthernet 0/3 Add a description to FastEthernet 0/24 Save the switch changes Hide Details Save the hostname Save the FastEthernet 0/1 description Save the FastEthernet 0/2 description Save the FastEthernet 0/3 description Save the FastEthernet 0/24 description Change the router hostname to SFO Add
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a local course wants to study the number of rounds played by members on weekdays. He gathered the sample information shown below for 520 rounds. At the .05 significance level, is there a difference in the number of rounds played by day of the week? 2. An auditor for American Health Insurance reports that 20% of policyholders submit a claim during the year. 15 policyholders are selected randomly. What is the probability that at least 3 of them submitted a claim the previous year? 3. When a class
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Chapter 9 Monopoly As you will recall from intermediate micro, monopoly is the situation where there is a single seller of a good. Because of this, it has the power to set both the price and quantity of the good that will be sold. We begin our study of monopoly by considering the price that the monopolist should charge.1 9.1 Simple Monopoly Pricing The object of the firm is to maximize profit. However, the price that the monopolist charges affects the quantity it sells. The relationship
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able to: • formulate simple linear programming problems in terms of an objective function to be maximized or minimized subject to a set of constraints. • find feasible solutions for maximization and minimization linear programming problems using the graphical method of solution. • solve maximization linear programming problems using the simplex method. • construct the Dual of a linear programming problem. • solve minimization linear programming problems by maximizing their Dual. 0.1.2 Introduction
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close relationship between Counting/Combinatorics and Probability. In many cases, the probability of an event is simply the fraction of possible outcomes that make up the event. So many of the rules we developed for finding the cardinality of finite sets carry over to Probability Theory. For example, we’ll apply an Inclusion-Exclusion principle for probabilities in some examples below. In principle, probability boils down to a few simple rules, but it remains a tricky subject because these rules often
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question now arises: does any such function, m(.), exist? In selected settings the answer is, no doubt, affirmative. But, in general, the answer is negative. This is discussed below. THE IMPOSSIBILITY RESULT max A E(U I y, 7, ay*)D(y | X7EXc YEY (2) (2) Observe that this characterization of the choice, or specification, of an accounting alternative is but an expected utility variant of the situation initially discussed. We provide for comparison of any pair of alternatives; and our comparisons
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