$($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.