RatLand is a large family theme park located in central Texas. Over the years a visit to Ratland has been institutionalized as a prime "have to" experience for children growing up in America. Additionally, Ratland has developed a significant international following among Asians and the British, making it one of the prime international vacation destinations of any location on the globe. The Ratland experience is based on the various exploits of a group of loosely associated animal cartoon characters led by Schmutzig Rat and originally developed during the Great Depression. The Schmutzig franchise had become less popular as the years passed until brilliant marketing of the Ratland concept gave the characters new life in the 1960s. Now adults with fond memories of visiting Ratland as children bring their own children.
Ratland is planning for a new attraction scheduled to open in the Spring of 2016. (The opening will correspond with the 75th anniversary of the release of the first Schmutzig Rat cartoon.) "Rambo Squirrel's Wild 3-D Water Massacre Splash" will be a theater-based 3-D experience in which patrons will be brought into a 420-seat theater for a 12-minute presentation. The presentation will be a combination of film and live-action with real and computer-generated special effects. The height of the show will feature Rambo Squirrel mowing down his woodland friends all in fun with a semi-automatic super-soaker machine gun connected to a garden hose. (Rambo Squirrel Hose Guns will be available for purchase in an attached gift shop for more fun at home.)
In an average hour 950 Ratland patrons are expected to approach and join the line for the Rambo Squirrel attraction on a busy summer day. They will be brought into the theater in groups no larger than 420 to experience the 12-minute show, then are quickly ushered out of the theater and a new group is brought in. Emptying and refilling the theater is expected to take three minutes on average. The Rambo Squirrel Design Team is aware of how queues behave and understands the concept of an average waiting time in the queue. However, they would also like to know two other points:
a. The Design Team needs to plan for space around the attraction for the line of waiting patrons. Assuming 2.3 linear feet per person, how long should the line space be in order to be adequate 95% of the time on busy summer days?
b. What proportion of time will there be more than 1200 patrons viewing the attraction or waiting to view it?
c. To potentially reduce the length of the line at these peak times the Rambo Squirrel Design Team is considering two options: 1) The producer can drop one scene from the show which will shorten the performance by 45 seconds, or 2) The staff can bring in 75 temporary seats to increase the theater's capacity. Which option will give the greatest reduction in line space that needs to be set aside to accommodate the line 97% of the time on a busy summer day.