A jewelry firm buys semiprecious stones to make bracelets and rings. The supplie
ID: 461922 • Letter: A
Question
A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $8.7 per stone for quantities of 600 stones or more, $9.5 per stone for orders of 400 to 599 stones, and $10 per stone for lesser quantities. The jewelry firm operates 199 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 26 percent of unit cost, what is the optimal order size? (Round your intermediate calculations to the nearest whole number.)
If lead time is 3 working days, at what point should the company reorder? (Round your intermediate calculations to the nearest whole number.)
A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $8.7 per stone for quantities of 600 stones or more, $9.5 per stone for orders of 400 to 599 stones, and $10 per stone for lesser quantities. The jewelry firm operates 199 days per year. Usage rate is 25 stones per day, and ordering costs are $48.
Explanation / Answer
a. Annual Usage = 25*199 = 4975 stones per year
EOQ = (2*Annual usage*Ordering cost / Carrying cost )^0.5 = (2*4975*48/2)^0.5 = 489 stones
We see that total cost associated with EOQ = 48,240
Lets us also determine the total cost associated with lowest slab of price , i.e. $ 8 for 600 units and above
Total cost is lowest in case of order quantity of 600.
Therefore to minimise the total annual cost, optimal order size = 600 stones per order
b). The optimal order size still remains the same,
c). Reorder Point (ROP) = Leadtime Demand = 25*3 = 75 stones. Therefore the company should place the order, when the inventory level is 75 stones.
Formulas for calculating Ordering cost = Annual Usage/ Order qty * Cost per order
Carrying cost = Order qty / 2 * Carrying cost per unit
Units Unit Cost Total Cost Material Cost 4,975 9.5 47,263 Ordering Cost 10 (number of orders) 48 489 Carrying Cost 244 (average inventoy) 2 489 Total 48,240Related Questions
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