A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $8.10 per stone for quantities of 600 stones or more, $8.50 per stone for orders of 400 to 599 stones, and $9.00 per stone for lesser quantities. The jewelry firm operates 110 days per year. Usage rate is 28 stones per day, and ordering costs are $48. a. If carrying costs are $2 per year for each stone, find the order quantity that will minimize total

annual cost.

b. If annual carrying costs are 30 percent of unit cost, what is the optimal order size?

c. If lead time is six working days, at what point should the company reorder?

a.385 stones

b.349 stones

c.168 stones

Explanation:

Order quantity that minimizes total annual cost is known as the Economic Order Quantity.

Economic Order Quantity = √(2 × Annual Demand × Ordering Cost per Order) / Holding Cost per unit

                                           = √(2×28×110×$48) / $2

                                           = 384.5 or 385 stones

Economic Order Quantity = √(2 × Annual Demand × Ordering Cost per Order) / Holding Cost per unit

                                           = √(2×28×110×$48) / ($8.10 × 30%)

                                           = 348.8 or 349 stones

Re-oder point is the point at which the order should be placed to obtain additional inventories

Reorder Point = Lead Time × Usage

                        = 6 days × 28 stones

                        = 168 stones

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