Question: The Children's Theater Company is a nonprofit corporation managed by Shannon Board. The theater performs in two venues: Kristin Marie Hall and the Lauren Elizabeth Theater. For the upcoming season, seven shows have been chosen. The question Shannon faces is how many performances of each of the seven shows should be scheduled. A financial analysis has estimated revenues for each performance of the seven shows, and Shannon has set the minimum number of performances of each show based on union agreements with Actor's Equity Association and the popularity of the shows in other markets. These data are shown in the table at the right.
Kristin Marie Hall is available for 60 performances during the season, whereas Lauren Elizabeth Theater is available for 150 performances. Shows 3 and 7 must be performed in Kristin Marie Hall, and the other shows are performed in either venue.
The company wants to achieve revenues of at least $550,000 while minimizing its production costs. Develop and solve a linear optimization model to determine the best way to schedule the shows. Is it possible to achieve revenues of $600,000? What is the highest amount of revenue that can be achieved?
Minimum Number
Show Revenue Cost of Performance
1 $2,217 $ 968 32
2 $2,330 $1,568 13
3 $1,993 $ 755 23
4 $3,364 $1,148 34
5 $2,868 $1,180 35
6 $3,851 $1,541 16
7 $1,836 $1,359 21