A vending company supplies food to a large university. Because students often kick the vending machines out of anger and frustration, the management has a constant repair problem. The machines break...

A vending company supplies food to a large university. Because students often kick the vending machines out of anger and frustration, the management has a constant repair problem. The machines break down on an average of three per hour and the break downs are distributed in a Poisson manner. Down time costs the company 25 dollars per hour per machine, and each maintenance worker is paid 4 dollars per hour.One worker can service machines at an average rate of five per hour, distributed exponentially; two workers working together can service seven machines per hour, distributed exponentially; and a team of three workers can do eight per hour, distributed exponentially. What is the optimal maintenance crew size for servicing the machines? [8 marks]