College freshman Jon Jackson wants to plan his Saturday night schedule for the next three weekends. In particular, he wants to determine what to do between 8:00 p.m. until 2:00 a.m. each Saturday night. He has narrowed his choices to three possible activities each evening, and he has assigned “utils” (i.e., happiness points on a scale of 1−10, with 10 being best) to each of those activities. Jon loves to watch TV because it relaxes him after a tough week at school, so he assigns 9 utils per hour of television watching. In addition, he is a serious student, so he assigns studying a value of 8 per hour in each of the first two weeks and 10 per hour during week 3 (because there is an exam the following Monday). Finally, Jon hates college parties because he doesn’t like loud music, but his girlfriend always wants him to join her at her sorority parties. Jon assigns 2 utils per hour of partying in weeks 1 and 3 and 4 utils during week 2 (because at least ice cream will be served at the week 2 party). After careful thought, Jon has come up with the following restrictions for his problem:

(1) Total hours spent on activities each night must equal the 6 hours available.

(2) He won’t study more than 4 hours per night during either of the first two weeks (he doesn’t want to be perceived as being a complete nerd).

(3) He must study at least 3 hours in the third week (he wants to score well on the upcoming exam).

(4) He must study at least 10 hours over the 3-week period (he wants to maintain a high grade-point average).

(5) He must average at least 1 hour per week of TV watching (he is forcing himself to relax).

(6) He must party at least 2 hours over the next 3 weeks (he wants to keep his girlfriend happy).

(7) He will never spend more than 3 hours at a party (he is concerned about long-term hearing loss). 

What allocation of time will maximize Jon’s happiness while satisfying his various requirements?