3. A manufacturing plant requires ten-penny nails to produce its product. If it runs out of the nails the whole plant shuts down. The company uses 15,000 nails per year. Order costs are $25 per order and carrying costs are $0.02.

a. What is the optimal order quantity?

b. Assume that the firm wants a safety stock of 3,000 nails. What will the first order be and what will each subsequent order be?