For each problem, clearly state your defined variables and equations. Round all numbers to at least $2$ decimal points. Submit only $1$ Word or PDF file.

$1.($Process analysis $40$ pts$.)$

Galahad, the owner of a small dry$-$cleaning service, wants you to help optimize his business. First, the receptionist takes $5$ minutes to receive payment for a load of clothing, collect the clothing and note any stains or tears. The clothing load is then placed into one of four washing machines, taking $25$ minutes each. Two employees then iron the clothing, taking typically $15$ minutes for each load.

a$)$ What is the capacity of the process in terms of loads, and which step is the bottleneck?

b$)$ What is the average theoretical flow time for one load to go through the entire process $($i$.$e$.,$ without including

waiting$)?$

c$)$ Galahad would like to hire another employee at the ironing step. If the additional employee costs $$25\mathrm{.}00$ per

hour, and profit averages $$12\mathrm{.}00$ per customer load, should Galahad hire the new employee? Assume demand is $10$ customer loads per hour.

$2.($Process analysis $30$ pts$.)$

To prepare for a festival$$s potluck, Griselda decides to make homemade falafel. After a grueling three hours, she manages to fry a total of $270$ falafels.

a$)$ Her pot size currently fries $20$ falafels at a time. How long is each falafel fried for? Hint think of the pot as the amount of inventory in our system.

b$)$ Griselda is considering purchasing a larger pot that can fry as many falafels as she wants per batch. To cook them to perfection, each batch of falafels is fried for $12$ minutes. If she wants to continue producing falafels at her current rate of $270$ per $3$ hours, how many falafels on average should be fried per batch? Should she purchase a larger pot?

$3.($Quality analysis $30$ pts$.)$

Walter is a chemical engineer that is monitoring the production of a common cleaning solution in being able to remove germs. Walter measures the germ level of $12$ batches each day of the week to determine whether the process is in control or not. Historically, the cleaning product is working fine if the average germ rate is $20$ parts per million and the range is $1\mathrm{.}5$ parts per million $($germ levels that are too high or low are both indicators that the process is out of control. $($Note: if $$ is needed, let $=3).$

$20\mathrm{.}44$ Germ range $($ppm$)0\mathrm{.}732\mathrm{.}881\mathrm{.}032\mathrm{.}350\mathrm{.}402\mathrm{.}620\mathrm{.}32$

a$)$ Which two types of control chart should be used? Hint: use the most standard charts for this type of process.

b$)$ For each of your two charts,

a$.$ What is the upper control limit$?$ b$.$ What is the lower control limit$?$ c$.$ Draw the chart.

c$)$ After viewing both charts, do you think the process is $($more likely$)$ in control or not?