Assignment:
Connecticut Tanning has two tanning beds. One bed serves the company’s regular members exclusively. The second bed serves strictly walk-in customers (those without appointments) on a first-come, first-served basis. Orv Karan, the store manager, has noticed on several occasions during the busy 5 hours of the day (2:00 p.m. until 7:00 p.m.) that potential walk-in customers will most often walk away from the store if they see one person already waiting for the second bed. He wonders if capturing this lost demand would justify adding a third bed. Leasing and maintaining a tanning bed costs Connecticut Tanning $600 per month. The price paid per customer varies according to the time in the bed, but Orv has calculated the average net income for every 10 minutes of tanning time to be $2. A study of the pattern of arrivals during the busy hours and the time spent tanning has revealed the following:
| Time between arrivals(minutes) |
Probability |
Time in Tanning (Minutes) |
Probability |
|
| 5 |
0.3 |
10 |
0.2 |
|
| 10 |
0.25 |
15 |
0.3 |
|
| 15 |
0.2 |
20 |
0.4 |
|
| 20 |
0.15 |
25 |
0.1 |
|
| 25 |
0.1 |
|
|
|
a) Simulate 4 hours of operation (arrivals over 4 hours). Use the 14th column of Table for arrival times and the 8th column for tanning times. Assume there is one person who has just entered the bed at 2:00 p.m. for a 20-minute tan. Indicate which customers balk at waiting for the bed to become available. How many customers were lost over the 4 hours (the simulation ends at 6:00 p.m.)?
b) If the store is open an average of 24 days a month, will capturing all lost sales justify adding a new tanning bed?
Provide complete and step by step solution for the question and show calculations and use formulas.