Sally\'s Silk Screening produces specialty T-shirts that are primarily sold at s

Question

Sally's Silk Screening produces specialty T-shirts that are primarily sold at special events. She is trying to decide how many to produce for an upcoming event. During the event itself, whcih lasts one day. Sally can sell T-shirts for $20 apiece. However, when the event ends, any unsold T-shirts are sold for $4 apiece. It costs Sally $8 to make a specialty T-shirt. Using Sally's estimate of demand that follows, how many T-shirts should she produce for the upcoming event? Please show work
Demand                 Probability
300                           0.05
400                            0.10
500                            0.40
600                            0.30
700                            0.10
800                            0.05

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

b) How many T-shirts should she produce for the upcoming event?

Explanation / Answer

a)
12/20=.6

b)
300*.05+400*.1+500*.4+600*.3+700*.1+800*.05= 545

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