Problem:

Father's Cookies produces chocolate-chip cookies in a large oven that holds up to 2,000 pounds of cookies at a time. Annual demand is constant at 200,000 pounds; variable cost is $.25 per pound. Oven cleanout is required after the oven processes 2,000 or fewer pounds in a batch (i.e., each time the oven is used); the cleanout takes one hour's time for four workers, each of whom is paid $7 per hour. Assume that multiple batches can be produced one after the other (i.e., production is not capped at 2,000 lbs). For example, at t=0 multiple batches can be produced nearly instantaneously; however, each batch will require a cleanout. The inventory holding cost is 20 percent per dollar per year; spoilage occurs if inventory is held by Father's Cookies more
than 12 months. There is substantial unused oven capacity.

Required:

In what quantity should these cookies be produced? Why? Solve the given numerical problem and illustrate step by step calculation.