Airport Massage Station
A small company just opened a new massage station at Philadelphia airport. The company has a stand that offers massages to travelers. Customers can select a length of massage between 5 and 20 minutes and there is a unique rate of $30 independently of the length selected by customers. The average length of massage requested by customers is of 15 minutes with standard deviation of 10 minutes.
There are four employees delivering massages. The average number of potential customers requesting a massage is of 20 per hour. The inter-arrival times are assumed to be exponentially distributed.
If no spot is available when the customer arrives, s/he leaves in order not to risk missing her/his flight.
-The station manager is considering the option of hiring additional employees to deliver massages.The hourly wage of an employee is $50/hr.How many ADDITIONAL employees should s/he hire if s/he wants to maximize profits? [Profit = revenues from customers - labor cost] Suppose that there exists sufficient equipment to accommodate as many new employees as needed.
A)none
B)1 additional employee
C)2 additional employees
D)3 additional employees
E)4 additional employees

Question

Quizplus · Accepted Answer

The optimal number of additional employees to hire is 2. This is because the profit is maximized when the number of customers served per hour is equal to the number of employees. In this case, the average number of customers requesting a massage is 20 per hour, so the optimal number of employees is 20 / 30 = 2.

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