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. Show Revenue Cost Minimum Number of Performances $1$ $$2,217$ $$968322$ $$2,330$ $$1,568133$ $$1,993$ $$755234$ $$3,364$ $$1,148345$ $$2,868$ $$1,180456$ $$3,851$ $$1,541167$ $$1,836$ $$1,35921$ 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 Lauren Elizabeth Theater, 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. $(19$ points$)$