(Production Lot Size model)Beauty Bar Soap is produced on a production line that has an annual capacity of 50,000 cases.The annual demand is estimated at 28,000 cases, with the demand rate essentially constant throughout the year. The cleaning, preparation, and setup of the production line cost approximately $145.The manufacturing cost per case is $5.50, and the annual holding cost is figured at a 24% rate. Other relevant data include 250 working days per year.How much is the optimal production quantity? How much is the percentage of the machines being used (machine utilization)? How much will be the annual holding cost? And annual set up cost? An explanation of formulas would be helpful.