Consider the problem faced by a summer camp recreation director who is trying to choose activities for a rainy day. Information about possible choices is given in the table below. Category Activity Time Popularity Popularity with (minutes) with Campers Counselors Art 1 - Painting 30 4 2 2 - Drawing 20 5 2 3 - Nature craft 30 3 1 Music 4 - Rhythm band 20 5 5 Sports 5 - Relay races 45 2 1 6 - Basketball 60 1 3

Computer 7 - Internet 45 1 1 8 - Creative writing 30 4 3 9 - Games 40 1 2 a. The popularity ratings are defined so that 1 is the most popular. If the objective is to keep the campers happy, what should the objective function be? Write constraints for these restrictions: b. At most one art activity can be done. c. No more than two computer activities can be done. d. If basketball is chosen, then the music must be chosen. e. At least 120 minutes of activities must be selected. f. To keep the staff happy, the counselor rating should be no higher than 10.