Using your excel sheet to show your answers and math to the following$$ problem:

You are managing a ice cream kiosk that sells prepackaed ice creams and frozen juice bars at a farmers market with many vendors selling various food$$ items, including cold refreshments. You have received some feedback from the management of the Farmers Market that your$$ "service is$$ slow" and they have watched customers balk.

You gather some data to start to assess the data. Since you are only open Saturday and Sunday you believe that most days the customer arrival rates per hour are pretty similar. On$$ average, you served $400$ customers each day during a $5$ hour day of business.

You observe the staff$-$ work to understand their capacity and what a typical orders look like$($one serving, multiple$$ servings$)$ to better understand the complexity of the work. You estimate that the team on average can serve $110$ customers per hour.

Answer the following$($and show your$$ math$)$ on your spreadheet

$1.$ What is the average utilization of the system expressed in$$ percent? Does this seem a reasonable$$ number? Why or why$$ not? Think of the answer from the employees perspecive and how the utlization may reflect the brand.

$2.$ Given the Farmers Market is popular with both vendors and$$ customers, the management is concerned that the lines spill into the walk way making it hard for people to move around. Based on this space you estimated that by the time you have four customers in$$ line, they are getting close to standing in the walk way. What is the probability for this to happen. Is it a concern of yours based on the$$ answer?

$3.$ Given some complaints about slow service you wanted to understand the time spent in line versus time spent in the entire system. Express your answer in MINUTES for both values$($and include which one is in line versus in the$$ system$)$

$4.$ Given the concerns with the line length you want to be able to share with the market manager what the line looks like most days. What is the AVERAGE number of customers in the system versus the AVERAGE number of customers in line.

Provide in writing your perspective about the situation and how you would reply to the market$$ manager?

EXTRA QUESTION $+2$ points

If you added scooped ice cream to your$$ menu, what type of service facility would this now$$ be$?$ Why? Would the same model work to estimate line lengths and$$ times?