7) PROBLEM 7 (14 marks) 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. Popularity ratings Time Popularity ratings with Category Activity (minutes) with Campers Counselors Art 1 - Painting 30 4 2 2 - Drawing 5 3 - Nature craft 30 Music 4 - Rhythm band Sports 5 - Relay races 45 6 - Basketball 60 3 Computer 7 - Internet 45 8 - Creative writing 30 9 - Games 2 20 NU A 20 NUNN 1 2 40 a) Give a general definition of the variables necessary in this problem so that each activity can be considered for inclusion in the day's schedule. (3) b) The popularity ratings are defined so that 1 is the least popular. If the objective is to keep the campers happy, what should the objective function be? (2) OPER-5002E - Management Sciences Finance & Operations, Laurentian University, Instructor Dr. Pawoumodom M. TAKOUDA (mtakouda laurentian.ca) Page 5 of 5 Write constraints for these restrictions: c) At least one sport activity shall be done. (1.5) d) No more than two art activities can be done. (1.5) e) If basketball is chosen, then the music must be chosen. (1-5) f) At most 180 minutes of activities must be selected. (1-5) g) A minimum of 65 minutes of activities shall be selected. (1-5)