Problem 1 Suppose Prof. are asked to optimize his trip. He has decided to spare 2 hours from his busy schedule to do some fun stuff. He has 5 activities to choose from: playing tennis, reading optimization books, watching football games, jogging on the street, and playing music. The table below lists the "utility" he receives for each activity (suppose each activity takes 1 hour), and the amount of energy consumed per hour by each activity. planning for a beach trip for summer vacation. Now you Activity 1. tennis 2. reading 3. watching football 4. jogging 5. music Utility (Units) 22 16 20 25 18 Energy (kCal) 35 20 20 40 He does not want to get too tired from his trip, so he wishes to use at most 60 kCal of energy. To limit the time using his eyes, Prof. Song decided that if he chose reading, then he could not go watching football games. 1. Formulate an integer program to help Prof. Song determine how to maximize his utility during his fantasy trip. 2. Solve this integer program in Excel or Python.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Problem 1 Suppose Prof.
are asked to optimize his trip. He has decided to spare 2 hours from his busy schedule to do some
fun stuff. He has 5 activities to choose from: playing tennis, reading optimization books, watching
football games, jogging on the street, and playing music. The table below lists the "utility" he
receives for each activity (suppose each activity takes 1 hour), and the amount of energy consumed
per hour by each activity.
is planning for a beach trip for summer vacation. Now you
Activity
1. tennis
2. reading 3. watching football
4. jogging 5. music
Utility (Units)
22
16
20
25
18
Energy (kCal)
35
20
20
40
He does not want to get too tired from his trip, so he wishes to use at most 60 kCal of energy. To
limit the time using his eyes, Prof. Song decided that if he chose reading, then he could not go
watching football games.
1. Formulate an integer program to help Prof. Song determine how to maximize his utility during
his fantasy trip.
2. Solve this integer program in Excel or Python.
Transcribed Image Text:Problem 1 Suppose Prof. are asked to optimize his trip. He has decided to spare 2 hours from his busy schedule to do some fun stuff. He has 5 activities to choose from: playing tennis, reading optimization books, watching football games, jogging on the street, and playing music. The table below lists the "utility" he receives for each activity (suppose each activity takes 1 hour), and the amount of energy consumed per hour by each activity. is planning for a beach trip for summer vacation. Now you Activity 1. tennis 2. reading 3. watching football 4. jogging 5. music Utility (Units) 22 16 20 25 18 Energy (kCal) 35 20 20 40 He does not want to get too tired from his trip, so he wishes to use at most 60 kCal of energy. To limit the time using his eyes, Prof. Song decided that if he chose reading, then he could not go watching football games. 1. Formulate an integer program to help Prof. Song determine how to maximize his utility during his fantasy trip. 2. Solve this integer program in Excel or Python.
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