1. A car wash with 5 automated bays has a service rate of 10 cars per hour. The service rate follows a negative exponential distribution. Cars arrive at a rate of 24 cars per hour. The arrival rate follows a Poisson distribution. What is the total system cost if each car in the system has a waiting cost of $40 per hour and each automated bay costs $50 per hour to operate?

Show work either as equations or insert a table. Calculate final answer to two decimal places.

2. Compute the trend adjusted exponential smoothing forecast for period 3. Calculate your answer to 3 decimal places.

Alpha = 0.35 Beta = 0.40

Period	1	2	3
Actual	54	63	65
Base	53
Trend	5
Forecast

3. An industrial engineering team is setting up a work measurement project to examine how much time during the week a particular workstation is idle. Team members will check on the workstation at random times during the week and make note as to if the workstation is idle or not. The goal is to determine the estimated proportion of time the workstation is not processing any parts. Their goal is to find the proportion with a 95% confidence level and an error of +/- 5%.

Determine the sample size necessary for the project. Round answer up to the nearest whole number.