Boilermaker Land theme park conducts free tours of the engineering department that designs its rides. The tour times are not scheduled; they begin whenever there are a sufficient number of patrons wanting to take a tour. The arrival of patrons wanting a tour is well modeled as a renewalarrival process with expected time between arrivals of 1 minute. It costs Boilermaker Land $10 each time it conducts a tour, regardless of how many people are in the tour group. But there is also a cost to Boilermaker Land of having patrons waiting for a tour, because if they are waiting, then they are not spending money in the park. Accountants have estimated that patrons in the park spend money at the rate of $0.50 per minute. (a) What should the size of each tour group be to minimize long-run cost to Boilermaker Land? (Hint: Use the renewal-reward theorem to solve this problem, with waiting and tour costs being the rewards and the beginning of each tour being the renewal process. Let n be the size of each tour group, and notice that the nth patron to arrive for a tour incurs no waiting cost, the (n — 1)st incurs an expected waiting cost of (1 minute)($0.50 per minute), the (n — 2)d incurs an expected waiting cost of (2 minutes)($0.50 per minute), and so on.) (b) What is the expected time between the departure of tours for your optimal-size tour group?