Blue Baker 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 $$525.$ 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 $5,100$ pies. Determine the following: $(10$ points$)$