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(a) When you solve an integer programming problem (suppose it is a maximization prob- lem), how do you obtain an upper bound on the optimal objective value? How do you obtain a lower bound? (b) Suppose you use a binary variable yA to represent whether or not event A will happen, and use a binary variable yYB to represent whether or not event B will happen. How do you model the following logic constraint using an inequality? If A happens → then B must happen

(a) When you solve an integer programming problem (suppose it is a maximization prob- lem), how do you obtain an upper bound on the optimal objective value? How do you obtain a lower bound? (b) Suppose you use a binary variable yA to represent whether or not event A will happen, and use a binary variable yYB to represent whether or not event B will happen. How do you model the following logic constraint using an inequality? If A happens → then B must happen

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 33E
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(a) When you solve an integer programming problem (suppose it is a maximization prob- lem), how do you obtain an upper bound on the optimal objective value? How do you obtain a lower bound? (b) Suppose you use a binary variable yA to represent whether or not event A will happen, and use a binary variable yB to represent whether or not event B will happen. How do you model the following logic constraint using an inequality? If A happens then B must happen (c) In class we talked about how to model constraints like "either condition A holds or condition B holds (or both)". How about when you have three conditions? For example, how to model "at least one of the following three conditions should hold": (i) 3x1+x2 > 5; (ii) 2x1+2x2 > 4; (iii) x1+3x2 > 5? (If you use big-M inequalities here, you do not need to specify the values for the big-M parameters.)
Transcribed Image Text:(a) When you solve an integer programming problem (suppose it is a maximization prob- lem), how do you obtain an upper bound on the optimal objective value? How do you obtain a lower bound? (b) Suppose you use a binary variable yA to represent whether or not event A will happen, and use a binary variable yB to represent whether or not event B will happen. How do you model the following logic constraint using an inequality? If A happens then B must happen (c) In class we talked about how to model constraints like "either condition A holds or condition B holds (or both)". How about when you have three conditions? For example, how to model "at least one of the following three conditions should hold": (i) 3x1+x2 > 5; (ii) 2x1+2x2 > 4; (iii) x1+3x2 > 5? (If you use big-M inequalities here, you do not need to specify the values for the big-M parameters.)
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