Wallace Publishers has a large number of employees who use the company’s single fax machine. Employees arrive randomly t

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Wallace Publishers has a large number of employees who use thecompany’s single fax machine. Employees arrive randomly to use thefax machine at an average rate of 20 per hour. This arrival processis approximated by a Poisson distribution. Employees spend anaverage of two minutes using the fax machine, either transmittingor receiving items. The time spent using the machine is distributedaccording to a negative exponential distribution. Employees line upin single file to use the machine, and they obtain access to it ona firstcome, first-served basis. There is no defined limit to thenumber who can line up to use the machine. Management hasdetermined that by assigning an operator to the fax machine ratherthan allowing the employees to operate the machine themselves, itcan reduce the average service time from the current 2 minutes to1.5 minutes. However, the fax operator’s salary is $8 per hour,which must be paid 8 hours per day even if there are no employeeswishing to use the fax machine part of the time. Management hasestimated the cost of employee time spent waiting in line and atthe fax machine during service to be 17¢ per minute (based on anaverage salary of $10.20 per hour per employee). Should the firmassign an operator to the fax machine?