Alice N. Wunderlund manages the Mad Hatter store at Disneyland. This store sells novelty hats to tourists, especially the ever-popular Mickey Mouse Ears hat. Any hat purchased by patrons is monogramed for free. The store has one computer controlled sewing machine with an operator that sews the monograms one at time. The machine can sew an average of 20 hats per hour. Allice sells a hat requiring a monogram on the average once every 5 minutes.

a. What is the expected wait time for a hat before the sewing starts?

b. What is the average time to get a hat monogramed (wait time plus sewing)?

c. What is the average number of hats waiting to start the monogram?

d. What proportion of the time is the monogram machine busy?

e. Alice currently reduces the purchase price of the hat by 50 cents for each minute (\$30 per hour) that the purchaser has to wait before the sewing begins? Write the expression for the expected hourly discount that results from this policy?

f. Alice is considering replacing the policy in e. with a credit of \$2 per hat the hat has to wait at all before sewing begins on it? Write the expression the expected hourly discount that results from this policy?

Part 6FormulaAverage rate of hat arrival per mins(λ)requiring a monogram on the average 0.3333333333 20/60Average service time per hat inminutes 0.2 1/51/Average service time5 per hat…