Response to the following problem:
Mother Smith's Pies produces frozen fruit pies for sale to local restaurants. Demand for one of its best sellers, apple, averages 150 pies per day. The company's production facility is capable of producing 50 pies per hour and operates eight hours a day, seven days a week. The pies cost $2.25 to produce, and Mother Smith's estimates that its annual holding cost rate is 2 0 %. Because whenever a new type of pie is produced the machinery must be thoroughly cleaned, the cost of a production setup is estimated to be $90.
Determine the optimal production quantity of apple pies.