The Simple Simon Bakery produces fruit pies for freezing and subsequent sale. The bakery, which operates 5 days per week, 52 weeks per year, can produce pies at the rate of 64 pies per day. The bakery sets up the pie production operation and produces until a predetermined number (Q) of pies has been produced. When not producing pies, the bakery uses its personnel and facilities for producing other bakery items. The setup cost for a production run of fruit pies is $500.
The cost of holding frozen pies in storage is $5 per pie per year. The annual demand for frozen fruit pies, which is constant over time, is 5,000 pies. Determine the following:
a. The optimal production run quantity (Q)
b. The total annual inventory costs
c. The optimal number of production runs per year
d. The optimal cycle time (time between run starts)
e. The run length, in working days