A jewelry firm buys semiprecious stones to make bracelets and rings. The supplie
ID: 334959 • Letter: A
Question
A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of 58.40 per stone for quantities of 800 stones or more, $8.50 per stone for orders of 400 to 599 stones, and $10 per stone for lesser quantities. The jewelry firm operstes 222 days per year. Usage rate is 25 stones per day. and ordering costs are $43. a. If carrying costs are $2 per year for esch stone, find the order quantity that will minimize total annua cost. (Round your intermediate calculations and final answer to the nearest whole number.) Order quantity stones b. 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.) Optimal order sizeExplanation / Answer
Answer to question a :
Following details are provided :
Annual demand = D = 25 stones/ day x 222 days = 5550 stones
Ordering cost = Co = $48
Annual unit inventory cost = Ch = $2
Therefore economic order quantity ( EOQ ) which will minimize total annual ordering cost plus annual inventory carrying cost
= Square root ( 2 x Co x D / Ch )
= Square root ( 2 x 48 x 5550 / 2 )
= 516.139 ( 516 rounded to nearest whole number )
ORDER QUANTITY = 516 STONES
Answer to question b :
Annual demand = D = 25 stones / day x 222 days = 5550
Ordering cost = Co = $48
Since Carrying cost , Ch is proportional to price of the stone, Ch will change depending on respective quantity slab
Accordingly EOQ will also change depending on change in carrying cost
Following table presents different values of EOQ for different price levels and corresponding annual unit inventory carrying cost
Quantity
Price ( $)
Carrying cost- Ch ,$ ( 25% of Price )
EOQ ( rounded to nearest whole number)
1 – 399
10
2.5
462
400 – 599
8.5
2.125
501
600 or more
8.4
2.1
504
Out of above , it is only the EOQ of 501 which matches with its quantity slab of 400 -599 which it represents.
Therefore correct Economic Order quantity ( EOQ ) which minimizes total annual inventory carrying cost plus annual ordering cost ill be 501.
However we have to choose correct Order quantity which minimizes sum of annual purchasing cost , annual ordering cost plus annual inventory carrying cost .
We will compare above criteria for order quantity of 501 as well as order quantity of 600 which attracts lesser price than that for order quantity 501
Total cost for order quantity = 501 :
Annual purchasing cost = $ 5550 x 8.5 = $ 47175
Annual inventory carrying cost = Ch x order quantity /2 = 2.2125 x 501/2 = $554.23
Annual ordering cost = Co x D/order quantity = 48 x 5550/ 501 = $531.73
Total cost of all above = $4258.50 + $554.23 + $531.73 = $ 48260.96
Total cost for order quantity = 600 :
Annual purchasing cost = $5550 x 8.4 = $46620
Annual inventory carrying cost = $2.2125 x 600 /2 = $663.75
Annual ordering cost = Co x D / order quantity =$ 48 x 5550/600 = $444
Total cost for all above = $46620 + $663.75 + $444 = $47727.75
Since total cost for order quantity = 600 < Total cost for order quantity = 501 , optimal order size = 600
OPTIMAL ORDER SIZE = 600 STONES
ORDER QUANTITY = 516 STONES
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.