A jewelry firm buys semiprecious stones to make bracelets and rings. The supplie
ID: 389499 • Letter: A
Question
A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $8.90 per stone for quantities of 600 stones or more, $9.00 per stone for orders of 400 to 599 stones, and $10 per stone for lesser quantities. The jewelry firm operates 250 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 26 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 8 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 $8.90 per stone for quantities of 600 stones or more, $9.00 per stone for orders of 400 to 599 stones, and $10 per stone for lesser quantities. The jewelry firm operates 250 days per year. Usage rate is 25 stones per day, and ordering costs are $48.
Explanation / Answer
a. If carrying costs are $2 per year for each stone, find the order quantity that will minimize total annual cost.
Formula of economic order quantity (EOQ)
EOQ = Q = (2 * Annual Demand * Ordering cost/ Inventory holding cost)
Where,
Daily demand = 25 stones
Working days = 250 days per year
Therefore Annual demand, D = 25 * 250 = 6,250 stones
Ordering cost S = $48
Annual Inventory holding cost rate $2 per stone per year
Therefore
EOQ = Q = (2 * 6,250 *$48 / $2)
EOQ = Q = (300000) = 547.72 or 548 stones (rounding off to nearest whole number)
b. If annual carrying costs are 26 percent of unit cost, what is the optimal order size?
If Holding or carrying cost H = 26% of price per unit per annum
Case 1: The Cost = $10 if quantity ordered less than 400
Case 2: The Cost = $9.00 if quantity ordered between 400 to 599
Case 3: The Cost = $8.90 if quantity ordered equal to or more than 600
Holding or carrying cost H in Case 1,
26% of $10 = $2.60
Holding or carrying cost H in Case 2,
26% of $9 = $2.34
Holding or carrying cost H in Case 3,
26% of $8.90 = $2.314
For minimum cost, first we have to calculate Optimum Order quantity per order which is EOQ for each scenario
Case 1: EOQ = sqrt (2* D*S/H) = sqrt(2*6250*$48/$2.60) =480 stones (less than 400 units can be ordered at this price, therefore it is not possible)
Case 2: EOQ = sqrt (2* D*S/H) = sqrt(2*6250*$48/$2.34) = 506 stones (more than 400 units and less than 600 units can be ordered at this price, therefore it is possible)
Case 3: EOQ = sqrt (2* D*S/H) = sqrt(2*6250*$48/$2.314) = 509 stones (more than 600 units can be ordered at this price, therefore it’s not possible)
Therefore only possibility is case 2; the optimal order size is 506 stones
c. If lead time is 8 working days, at what point should the company reorder?
If demand and lead time are both constant then
The reorder point = Daily demand * lead time = 25 * 8 = 200 stones
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