Consider a middle school cafeteria. 90% of the students purchase both food and drinks (they first pick up food then drinks) and 10% of the students just buy a beverage. Assume that students arrive at a rate of 300 per hour and interarrival times follow an exponential distribution. 60% of the students who buy food purchase a hamburger. Three people work at that stand, and each takes on average 50 seconds to serve a customer. The remaining students purchase pizza. You may assume that no one purchases both a burger and pizza. One person works at the pizza stand and takes on average 30 seconds to serve a customer. There are four drink fountains, and customers spend on average 25 seconds at the fountain to get their drinks. All customers checkout at the registers. There are seven registers in parallel, it takes one minute to checkout a customer. Assume that all service times are exponential. a. On average, how long does a student who buys a hamburger and a drink spend at the cafeteria? b. On average, how many students are in the cafeteria? c. The school administration is striving to ensure that, on average, a student can leave the cafeteria with all their purchases in less than 10 minutes. Is the cafeteria currently meeting this goal?