Problem $20-9($Algo$)$

Sofia's Silk Screening produces specialty T$-$shirts that are primarily sold at special events. Sofia is trying to decide how many to

produce for an upcoming event. During the event, Sofia can sell T$-$shirts for $$48$ each. However, when the event ends, any unsold T$-$

shirts are sold for $$10$ each. It costs Sofia's $$22$ to make a specialty $T-$shirt. The company's estimate of demand is the following:

a$.$ What is the service rate $($or optimal fractile$)?$

Note: Round your answer to $2$ decimal places.

Service rate

b$.$ How many T$-$shirts should Sofia's produce for the upcoming event?