(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
Calculus: Early Transcendentals
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Chapter1: Functions And Models
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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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdcb50413-80d6-469c-93cd-08f16902242b%2F19f58d15-7656-4432-9bf2-54d1b4af6a53%2F8zbhqnr_processed.jpeg&w=3840&q=75)
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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