The Disney Imagineering Group has just designed a new attraction, and they have asked for your expert industrial engineering opinions. This ride is a simulator where the guest is a Jedi making first contact with Asgard. If a guest is staying in a resort on the property, they get to play through an extra part of the simulator and meet Professor X. Because it is interactive, the ride time for a customer ends up being exponential with a rate for = 7 for regular guests, and a rate of Mip = 4 for guests who stay on property. Approximately 30% of all guests stay on property. Based on its location, only three people can wait in line to ride, and only one person can ride it at a time. The Imagineers expect that the interarrival time between any two guests has a mean of 1/5. (a) Create a model for this system. Be sure to include how you define your state space, the list of events that can occur, the transition rate diagram, and the transition rate matrix. (b) Numerically solve for the steady state probabilities. (c) Application of Little's Law: i. What is the expected number of guests who are in the system? ii. What is the effective throughput rate? iii. How long on average do guests who decide to wait spend at this attraction before leaving? (d) The total cost of the simulator is both a function of the expected number in the system x and the type of customer in the simulator: Cr(x) = 15 + 40x2 if the customer in the simulator is a regular guest, and Cp (2) = 35 + 25x" if the customer in the simulator is a guest who stays on property. What is the expected total cost?