Question

Asked Apr 6, 2019

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A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $8.30 per stone for quantities of 600 stones or more, $9.40 per stone for orders of 400 to 599 stones, and $10 per stone for lesser quantities. The jewelry firm operates 175 days per year. Usage rate is 25 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. (Round your intermediate calculations and final answer to the nearest whole number.)

Order quantity _____________ stones

b. If annual carrying costs are 20 percent of unit cost, what is the optimal order size? (Round your intermediate calculations and final answer to the nearest whole number.)

Optimal order size ________ stones

Step 1

Calculating the value of the order quantity that will minimize total annual cost if carrying costs are $2 per year for each stone. We have,

Operation days = 175 days

Daily demand = 25 stones per day

Total annual demand (D) = 175 days x 25 stones per day = 4,375 days

Ordering cost (S) = $ 48 per order

Carrying cost(C) = $2 per year for each stone

Beginning with the lowest unit price, computation minimum points for each price range until you find a fea...

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