A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $8.20 per stone for quantities of 600 stones or more, $8.60 per stone for orders of 400 to 599 stones, and $9.10 per stone for lesser quantities. The jewelry firm operates 101 days per year. Usage rate is 19 stones per day, and ordering costs are $39. a. If carrying costs are $2 per year for each stone, find the order quantity that will minimize total annual cost. (Do not round intermediate calculations. Round your final answer to the nearest whole number.) Order quantity stones b. If annual carrying costs are 21 percent of unit cost, what is the optimal order size

Question

Business

Charlee Pratt

17 August, 09:37

A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $8.20 per stone for quantities of 600 stones or more, $8.60 per stone for orders of 400 to 599 stones, and $9.10 per stone for lesser quantities. The jewelry firm operates 101 days per year. Usage rate is 19 stones per day, and ordering costs are $39. a. If carrying costs are $2 per year for each stone, find the order quantity that will minimize total annual cost. (Do not round intermediate calculations. Round your final answer to the nearest whole number.) Order quantity stones b. If annual carrying costs are 21 percent of unit cost, what is the optimal order size

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Answers (1)

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Alfie · Answer 1

a. 274

b. 295

Explanation:

a. Optimum Order

Optimum Order = √ ((2*Total Annual Demand*Ordering cost per order) / Holding Cost per unit)

= √ ((2*101*19*$39) / $2)

= 273.57

= 274

b. Optimum Order

Optimum Order = √ ((2*Total Annual Demand*Ordering cost per order) / Holding Cost per unit)

= √ ((2*101*19*$39) / $8.20 * 0.21)

= 294.83

= 295