Customers at an amusement park arrive at the rate of 10 customers per hour.The entry booth is staffed by one employee.The mean service time at the booth to provide service to each customer is 5 minutes.The arrival rate follows a Poisson distribution,and the service time at the booth follows a negative exponential distribution.It is estimated that the cost of customer waiting time associated with dissatisfied customers and loss of goodwill is $15 per hour.The employee at the service booth is paid $10 an hour.Determine the total expected cost per day for the waiting line system.Assume total hours of operation as 10 hours per day.
A)$725
B)$625
C)$500
D)$100

Question

Quizplus · Accepted Answer

The total expected cost per day for the waiting line system includes the cost of customer waiting time and the cost of the employee at the service booth. Given that the cost of customer waiting time is $15 per hour and the employee is paid $10 an hour, we first calculate the customer waiting time cost and then add the employee's cost.1. Calculate the customer waiting time cost:- Arrival rate (λ) = 10 customers/hour- Service rate (μ) = 60 minutes/hour / 5 minutes/customer = 12 customers/hour- Operating hours = 10 hours/dayThe formula for the average number of customers in the system (L) for an M/M/1 queue is L = λ^2 / μ(μ - λ). Here, λ = 10 and μ = 12, so L = 10^2 / 12(12 - 10) = 100 / 24 = 4.17 customers.The average time a customer spends in the system (W) is L / λ = 4.17 / 10 = 0.417 hours/customer.The cost of customer waiting time per day = W * λ * Cost per hour * Operating hours = 0.417 * 10 * $15 * 10 = $625.2. Calculate the employee cost per day:Employee cost per day = $10/hour * 10 hours = $100.3. Total expected cost per day = Customer waiting time cost + Employee cost = $625 + $100 = $725.

Customers at an Amusement Park Arrive at the Rate of 10