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A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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2. True or False. You may state the reason for your choice for possible partial credits if your selection is incorrect (If you believe that your selection is correct, you do not need to write any explanation). You may assume that the direction of optimization is maximization in all these questions. (a) Let A and B be two formulations for an integer programming problem. Suppose the number of constraints of A is three times as many as B, and the number of variables of A is five times as many as B, then A will surely take more time to solve than B. (b) In an integer programming problem solved by the branch and bound algorithm, the gap between the upper bound and lower bound cannot increase during the course of the algorithm. (c) Let z1p be the optimal objective value of an integer programming problem, and let zLP be the optimal objective value of its linear programming relaxation, then zLP > ZIP. (d) To make sure that we have a valid integer programming formulation, if we use big-M, we want the big-M value to be as big as possible. (e) Integer programming problems can be solved by the simplex algorithm.
Transcribed Image Text:2. True or False. You may state the reason for your choice for possible partial credits if your selection is incorrect (If you believe that your selection is correct, you do not need to write any explanation). You may assume that the direction of optimization is maximization in all these questions. (a) Let A and B be two formulations for an integer programming problem. Suppose the number of constraints of A is three times as many as B, and the number of variables of A is five times as many as B, then A will surely take more time to solve than B. (b) In an integer programming problem solved by the branch and bound algorithm, the gap between the upper bound and lower bound cannot increase during the course of the algorithm. (c) Let z1p be the optimal objective value of an integer programming problem, and let zLP be the optimal objective value of its linear programming relaxation, then zLP > ZIP. (d) To make sure that we have a valid integer programming formulation, if we use big-M, we want the big-M value to be as big as possible. (e) Integer programming problems can be solved by the simplex algorithm.
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