Question

Mattera runs a cafeteria lunch service for their employees. Every Tuesday they offer individual portions of lasagna for $6.50 each. They buy the lasagna from Caitlin’s Kitchen for $4.00 apiece. They have been doing this for years, and history tells them that demand for lasagna follows a normal distribution with a mean of 600 portions and a standard deviation of 150 portions. Any leftovers at the end of the lunch period are sold to a local shelter for $2.00 per portion.

a. What is the probability that the demand for lasagna will be within 20% of expected demand?

b. How many portions of lasagna should Mattera order from Caitlin’s in order to maximize their expected profit?

c. If they order the quantity that you chose in part b, what is the probability that they will run out of lasagna at lunch?

d. Suppose that Caitlin’s production cost is $2.50 per portion. What order quantity will maximize the expected profit for the supply chain (i.e., Caitlin’s and Mattera working together)?

e. What is the minimum buyback price that Caitlin’s could offer Mattera in order to get them to order the optimal number of portions from part c?

Answer 1