Problem 2 (15 points) Two years ago, Panera Bread opened a franchise on Plymouth
ID: 355138 • Letter: P
Question
Problem 2 (15 points) Two years ago, Panera Bread opened a franchise on Plymouth Road. They bake their bread fresh every morning very early before the store opens, and they dont make more throughout the day. A loaf costs $2 to bake and can be sold to a customer for $5. Any loaves that are leftover at the end of the day can be donated to a local food bank and will have a $0.50 tax benefit. The manager, Ed, has been estimating how much to bake each day based on his expert judgment. However, the store has also been recording how many loaves of bread are ordered over the past several months, and he would like to start using this data to determine how much to bake. When Ed looks at the data, he notices that the number of loaves ordered on Tuesdays is uniformly distributed between 300 and 410 loaves. How many loaves should this Panera location bake on Tuesday mornings? Hint: the quantile function of an ?(a, b) is F-1 (t) = a + t(b-a).Explanation / Answer
Underage or shortage cost, Cu = Selling price - Cost = 5 - 2 = $ 3
Excess or Overage cost, Co = cost - salvage benefit = 2 - 0.5 = $ 1.5
Critical ratio = Cu/(Cu+Co) = 3/(3+1.5) = 0.667
Number of loaves this Panera location should bake = F-1(0.667) = a + 0.667*(b-a)
= 300 + 0.667*(410-300)
= 373 loaves