UltraFit Organic Foods orders many of its grocery items in lot sizes of 50 units. Average demand for organic coffee is 20,000 one-kilogram bags per year. Ordering cost is \($12.50\) per order, with an average purchasing price of \($8.\) Annual inventory carrying cost is \($1.50\) per one-kilogram bag of coffee.

a. What is the economic order quantity for coffee?

b. What are the annual cost savings if the shop orders the economic order quantity as opposed to the 50-unit lots?

c. If the coffee beans have a shelf life of only 90 days, what is the optimal order size?