9. A company can produce an item or buy it from a contractor. If it is produced, it will cost

$20 each time the machines are set up. The production rate is 100 units per day. If it is bought from a contractor, it will cost $15 each time an order is placed.The cost of maintaining the item in stock, whether bought or produced, is $.02 per unit per day. The company's usage of the item is estimated at 26,000 units annually. Assuming that no shortage is allowed, should the company buy or produce?

10. In Problem 8, suppose that shortage is allowed at a penalty cost of p per unit per unit time.

(a) Ifw is the maximum shortage during the inventory cycle, show that KD h{Y(1 -~) - wF + pw2 TCU(y,w) = - + (D)

Y 21-;y y* = /2KD(p + h)

Yph(l - ~)

2KDh(1 -~)

w* =

pep + h)

(b) Show that the EOQ results in Section 11.3.1 can be derived from the general formulas in (a).