A jewelry firm buys semiprecious stones to make bracelets and rings. The supplie
ID: 334400 • Letter: A
Question
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, $8.40 per stone for orders of 400 to 599 stones, and $10 per stone for lesser quantities. The jewelry firm operates 177 days per year. Usage rate is 25 stones per day, and ordering costs are $48.
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.)
If annual carrying costs are 25 percent of unit cost, what is the optimal order size? (Round your intermediate calculations and final answer to the nearest whole number.)
If lead time is 4 working days, at what point should the company reorder?
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, $8.40 per stone for orders of 400 to 599 stones, and $10 per stone for lesser quantities. The jewelry firm operates 177 days per year. Usage rate is 25 stones per day, and ordering costs are $48.
Explanation / Answer
Demand (D) = Number of days*Usage rate = 177*25 = 4425
Ordering cost (S) = 48
H = Carrying cost
EOQ = sqrt(2*D*S/H)
Total cost = D/EOQ*S + EOQ/2*H + Price*D
a) EOQ = sqrt(2*4425*48/2) = 461
b) Let us assume Carrying cost as 10
EOQ = sqrt(2*4425*48/10) = 206
Total cost = 4425/206*48 + 206/2*10 + 10*4425 = 46311
Assume EOQ of 400 and carrying cost 8.4
Total cost = 4425/400*48 + 400/2*8.4 + 8.4*4425 = 39381
Assume EOQ of 600 and carrying cost 8.2
Total cost = 4425/600*48 + 600/2*8.2 + 8.2*4425 = 39099
Hence EOQ = 600 units
c) Lead time = 4 days
Re-order quantity = Lead time*Usage rate = 4*25 = 100 stones
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