A jewelry firm buys semiprecious stones to make bracelets and rings. The supplie
ID: 445724 • Letter: A
Question
A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $8.4 per stone for quantities of 600 stones or more, $9.6 per stone for orders of 400 to 599 stones, and $10 per stone for lesser quantities. The jewelry firm operates 162 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 to the nearest whole number.)
If annual carrying costs are 21 percent of unit cost, what is the optimal order size? (Round your intermediate calculations to the nearest whole number.)
If lead time is 2 working days, at what point should the company reorder? (Round your intermediate calculations to the nearest whole number.)
If carrying costs are $2 per year for each stone, find the order quantity that will minimize total annual cost. (Round your intermediate calculations to the nearest whole number.)
Explanation / Answer
a)Economic Order Quantity = 2AB / CS
A=Annaul Consumption = 25 per day *162 = 4,050stones
B =Buying cost per Order=$48
C=Cost per Unit = 4,050 stones so it $8.4 per stone
S=Carrying Cost=$2
Economic Order Quantity = 2AB / CS
= 2 * 4,050 stones * $48 / $8.4 * $2
=$388,800 / $16.8
=23,143
=152 Stones
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b)Optimal Order Size
Economic Order Quantity = 2AB / CS
A=Annaul Consumption = 25 per day *162 = 4,050stones
B =Buying cost per Order=$48
C=Cost per Unit = 4,050 stones so it $8.4 per stone
S=Carrying Cost=$1.8($8.4 per stone * 21/100=$1.8)
Economic Order Quantity = 2AB / CS
= 2 * 4,050 stones * $48 / $8.4 * $1.8
=$388,800 / $15.12
=$25,714
=160 Stones
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c) The company reorder = Average Usage * Lead Time + Safety Stock
=499.50 * 2 +201 Stones
=1200 stones
Explanation:
Safety Stock
=Maximum - Average * Lead Time
= 600 - 499.50 * 2
=201 Stones
Average = 400 + 599/2=499.50
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