Question

A jewely firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $8.90 per stone for quantities of 600 stones or more, $9.30 per stone for orders of 400 to 599 stones, and $9.80 per stone for lesser quantities. The jewelry firm operates 108 days per year. Usage rate is 26 stones per day, and ordering costs are $406.
a.If carrying costs are $3 per year for each stone,find the order quantity that will minimize total annual cost. (Do not roun d intermediate calculations. Round your final answer to the nearest whole number) Order quantity stones _________
b. If annual carrying costs are 28 percent of unit cost, what is the optimal order size? (Do not round intermediate calculations. Round your final answer to the nearest whole number.) Optimal order size stones ___________
c. If lead time is 4 working days, at what point should the company reorder? (Do not round intermediate calculetions. Round your final answer to the nearest whole number) Reorder quantity stones ___________

Answer 1

Answer:

a. Order quantity that will minimize total cost = 503 stones

b. Optimal order size = 605 stones

c. Reorder point = 104 stones

Explanation:

Demand = 26 stones per day * 108 days = 2808 stones per year

a. Order quantity of Stones:

Economic Order Quantity = $\sqrt{2DS}/H$

D = Demand, S = Ordering Cost, H = Carrying Cost

= $\sqrt{2*2808*406}$ / 3

EOQ = 503 stones.

b. If Carrying cost is 28% of unit cost then EOQ:

= $\sqrt{2*2808*406}$ / 8.90* 0.28

= 1510 / 2.492 = 605 stones

c. Reorder Point:

= Average Usage per day * Average lead time + Safety stock

= 26 stones per day * 4 working days

= 104.