Question: (25 pts) A coffee shop in my neighborhood (it is not a Starbucks) has two different lines- one for customers ordering only drip coffee, and another for all other customers. Each line has its own server. The drip-coffee line gets on average 1 customer a minute; for these customers the average service time is 20 seconds and is virtually constant (at least for this problem). The other line gets on average 1 customer a minute and for these customers the average service time is 30 seconds (exponentially distributed). Assume that the arrival rates are Poisson distributed. For each of these lines, determine the average time in line (time spent waiting, not including service time) and average time in the system. Assuming that the employee is paid $12 per hour and the value the coffee shop places on customer waiting time is $8 per hour, calculate the total cost per hour for each of the systems. Please give, in your solution, the models used and the values for lambda and mu for each system.

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