3. The manager of a market can hire either Mary or Alice. Mary, who gives service at an exponential rate of 20 customers per hour, can be hired at a rate of $3 per hour. Alice, who gives service at an exponential rate of 30 customers per hour, can be hired at a rate of $C per hour. The manager estimates that, on the average, each customer’s time is worth $1 per hour and should be accounted for in the model.

Assume customers arrive at a Poisson rate of 10 per hour

(a) What is the average cost per hour if Mary is hired? If Alice is hired?

(b) Find C if the average cost per hour is the same for Mary and Alice.