Response to the following problem:
Archer Pharmaceuticals manufactures Tranquility brand sleeping pills, which have an average weekly demand of 25,000 bottles. The Archer factory operates 10 hours a day, six days a week. The production line at Archer Pharmaceuticals can produce 10,000 bottles of Tranquility daily. Archer's policy is to make a batch of Tranquility and, after building up sufficient inventory, use the production line to produce other products. The company estimates that setup for producing Tranquility pills takes about two hours and costs $325. It also estimates that the annual holding cost for a bottle of Tranquility is $0.55.
a. What is the optimal production batch size and the resulting total annual inventory holding and production setup cost of this policy?
b. What is the length of a production run in hours (including setup time)?
c. What is the number of calendar days between the start times of successive production runs? What assumptions did you make in solving this problem?