A jewelry firm buys semiprecious stones to make bracelets and rings. The supplie
ID: 347669 • 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, $8.60 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? (Do not round intermediate calculations. Round your final answer to the nearest whole number.)
Optimal order size stones
c. If lead time is 3 working days, at what point should the company reorder? (Do not round intermediate calculations. Round your final answer to the nearest whole number.)
Reorder quantity stones
Explanation / Answer
Given values:
For quantities (Q) > 600 stones, Price (P) = $8.20 per stone
(Q) = 400 to 599 stones, Price (P) = $8.60 per stone
(Q) < 400 stones, Price (P) = $9.10 per stone
Number of working days = 101 per year
Daily demand, d = 19 stones
Annual demand, D = 101 x 19 = 1919 stones
Ordering costs, Co = $39
Solution:
(a) Carrying costs, Ch = $2 per year
Total annual cost will be minimum at the Economic order quantitiy (EOQ). EOQ is determined using the below formula:
EOQ = 2DCo/Ch
where,
D = Annual demand
Co = Ordering costs
Ch = Carrying costs
Putting the given values in the above formula, we get;
EOQ = (2 x 1919 x 39)/2
EOQ = 273.57 or 274
Total annual cost will be minimum at order quantity of 274 stones
(b) Annual carrying cost = 21 percent of unit cost
Since, there are three different price slabs, the optimal order size will be determined for each price slab.
1) (Q) > 600 stones, Price (P) = $8.20 per stone:
Carrying cost, Ch = 21% of $8.20
Ch = $1.72
EOQ = 2DCo/Ch
EOQ = (2 x 1919 x 39)/1.72
EOQ = 294.99 or 295
EOQ = 295 stones
Not feasible, since EOQ falls below the applicable quantity slab of Q > 600.
2) (Q) = 400 to 599 stones, Price (P) = $8.60 per stone
Carrying cost, Ch = 21% of $8.60
Ch = $1.81
EOQ = 2DCo/Ch
EOQ = (2 x 1919 x 39)/1.81
EOQ = 287.57 or 288
EOQ = 288 stones
Not feasible, since EOQ falls below the applicable quantity slab of Q = 400 - 599.
3) (Q) < 400 stones, Price (P) = $9.10 per stone
Carrying cost, Ch = 21% of $9.10
Ch = $1.91
EOQ = 2DCo/Ch
EOQ = (2 x 1919 x 39)/1.91
EOQ = 279.94 or 280
EOQ = 280 stones (Feasible)
Optimal order size = 280 stones
(c) Lead time = 3 days
Reorder point is calculated as;
R = L x d
where,
L = Lead time
d = daily demand
R = 3 x 19
Reorder quantity = 57 stones
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