a.) 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. (i) What is the optimal order quantity? (ii) 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? b.) You start work at a new firm and learn that it is the company policy to never take a trade discount. When you ask your boss about this, she says that the firm needs the trade credit to avoid borrowing more money. You tell her it would be cheaper to borrow than to miss taking the discounts. She tells you to prove it. You learn that most of your suppliers offer terms of 1/20, net 30. Compute the effective annual rate and the annual percentage rate. If the firm's cost of borrowed funds is 15%, should it take the discounts?