You have taken a job as manager of Cupcake Heaven in Old Town Alexandria, Virginia. It is located on a busy street with lots of walk-in traffic. The owner, Sue, is thrilled at the prospect of you helping her analyze her operations. Cupcake Heaven currently operates in the following manner.
The baker arrives each morning at 5 am. It takes her 30 min to mix and bake a batch of cupcakes. A batch is 50 cupcakes. While a batch bakes she is cleaning up from the first batch and therefore cannot start a second batch until the first has finished baking. The decorator, who frosts and decorates the cupcakes, arrives at 5:30 am. It takes him 40 minutes to decorate a batch. The baker finishes baking at 10 am. She then finishes cleaning up, makes coffee for customers, takes inventory, and places a replenishment order to be delivered later that day for the next day’s baking. The store opens at 10 am and remains open until 8 pm. Some days the cupcakes sell out by 2 pm, other days they have leftovers. Averaging the demand for an entire day, they have found demand to be about 40 cupcakes per hour with a standard deviation of 5.
Sue wants you to answer the following questions for her.
a. What is the current daily capacity of the baking/decorating process? Is it sufficient to meet the daily average demand?
b. What is the maximum inventory level of cupcakes (in batches) waiting to be decorated?
c. What is the maximum length of time for which a batch of cupcakes will wait (in inventory) to be decorated? What time is the decorator finished decorating?
(PLEASE SHOW YOUR WORK)