Fairfield Mall $($Q$1-$Q$4)$

On a typical day, the Fairfield mall sees customers arriving at an average rate of $225$ per hour and each customer stays in the mall for an average of $135$ minutes.

Q$1.$ What is the average number of customers in the mall at any time?

Q$2.$ A third of all the customers come alone and make up$,$ on average, $22\%$ of the customers in the mall. How long in hours, on average, does a single customer $($who came alone$)$ spend in the mall?

Q$3.$ The other two$-$thirds come as family groups. Estimate the average time $($in hours$)$ a typical family spends in the mall.

Q$4.$ Assume that every single customer comes in a car and every family comes in one car. The mall has a $300-$car parking garage which they are able to electronically monitor and have observed that, on average, $80\%$ of the parking spots in the garage are occupied. What is the average family size?

Huffy Bicycle Company $($Q$5-$Q$7)$

Huffy Bicycle Company manufactures bicycles in Mexico and China and sells them in the U$.$S$.$ at a steady rate $1000$ bicycles per day. The time to ship a bicycle from Mexico is about three days on average and it is about $20$ days to ship the bicycles from China. Currently, $20\%$ of the bicycles are manufactured in Mexico and $80\%$ of the bicycles are manufactured in China.

Q$5.$ What is the average number of bicycles in transit?

Q$6.$ Huffy wants to change its production volumes in Mexico and China in order to ensure that its annual inventory turns are about $30.$ Assuming $360$ days per year, what is the new inventory level in transit?

Q$7.$ To achieve these inventory levels, what percentage $(\%)$ of the production should now be in China?$$

Salt Lake County Hospital $($Q$8-$Q$14)$

The Salt Lake County Hospital is assessing its Emergency Department $($ED$)$ capacity so it knows how to expand as the county population grows. The hospital has the following information about the ED:

Resource Number

Nurses $12$

Physicians $5$

X$-$ray Technicians $4$

Examination rooms $10$

Trauma bays $3$

On average, nurses need to spend $30$ minutes with each patient that comes in$.$ Additionally, physicians need to spend an average of $20$ minutes with each patient. Each technician can X$-$ray up to $5$ patients per hour. All patients have to go through one nurse, one physician and the X$-$ray.

Q$8.$ What is the total capacity of Nurses, as in the maximum number of patients the Nurses can see in one hour? Round your answer to one decimal place.

Q$9.$ What is the total capacity of Physicians, as in the maximum number of patients the Physicians can see in one hour? Round your answer to one decimal place.

Q$10.$ What is the total capacity of the X$-$Ray Technicians $($max number of patients that can be X$-$rayed in one hour$)?$ Round your answer to one decimal place.

Thereafter, the patients are parsed into two categories: $20\%$ of all patients that come into the ED are trauma victims that need to be placed in a trauma bay. The other $80\%$ of the patients go into normal examination rooms. Each trauma patient spends an average of $30$ minutes in a trauma bay before leaving the ED $($usually then being admitted to the main part of the hospital$),$ whereas non$-$trauma patients spend an average of $45$ minutes in an examination room before leaving the ED$.$

Q$11.$ Suppose on average $50$ patients come to the emergency department every hour. What is the implied utilization $($in $\%)$ at the trauma bays? Recall there are $3$ trauma bays. Round your answer to the nearest whole number.

Q$12.$ Suppose on average $50$ patients come to the emergency department every hour. What is the implied utilization at the examination rooms $($in $\%)?$ Recall there are $10$ examination rooms.

Q$13.$ Which resource is the bottleneck?

a$)$Examination Rooms

b$)$Nurses

c$)$Physicians

d$)$X$-$Ray Technicians

e$)$Trauma Bays

Q$14.$ Suppose we hired one more physician so that the total number of physicians becomes $6.$ What will be the capacity of the process, as in the maximum number of patients the Emergency Department can treat in one hour? Round your answer to one decimal place.