Problem 13-13 A mail-order house uses 15,975 boxes a year. Carrying costs are 42
ID: 435599 • Letter: P
Question
Problem 13-13 A mail-order house uses 15,975 boxes a year. Carrying costs are 42 cents per box a year, and ordering costs are $99. The following price schedule applies. Number of Boxes 1,000 to 1,999 2,000 to 4,999 5,000 to 9,999 10,000 or more Price per Box $1.45 1.35 1.25 1.20 a. Determine the optimal order quantity. (Round your answer to the nearest whole number.) Optimal order quantity boxes b. Determine the number of orders per year. (Round your answer to 2 decimal places.) Number of orderper yearExplanation / Answer
Solution:
Optimal Order Quantity (Q*) is calculated as,
Q* = SQRT [(2 x D x Co) / Cc]
where,
D = Annual demand
Co = Ordering cost
Cc = Carrying cost
Putting the given values in the above formula, we get;
Q* = SQRT [(2 x 15975 x 99) / 0.42]
Q* = 2744
Since, the Q* lies in the 2000 to 4999 bracket, the total costs needs to be compared at Q* and lower price breaks of 5000 and 10000 to seei which cost is the lowest.
1) Total cost at (Q* = 2744):
Total cost = Annual Ordering cost + Annual Carrying cost + Annual price
Total cost = [(Annual demand / Q) x Co] + [(Q / 2) x Cc] + (Annual demand x price per unit)
Total cost = [(15975 / 2744) x 99] + [(2744 / 2) x 0.42] + (15975 x 1.35)
Total cost = 576.36 + 576.24 + 21,566.25
Total cost = $22,718.85
2) Total cost at (Q* = 5000):
Total cost = [(15975 / 5000) x 99] + [(5000 / 2) x 0.42] + (15975 x 1.25)
Total cost = 316.31 + 1,050 + 19,968.75
Total cost = $21,335.06
3) Total cost at (Q* = 10000):
Total cost = [(15975 / 10000) x 99] + [(10000 / 2) x 0.42] + (15975 x 1.20)
Total cost = 158.15 + 2,100 + 19,170
Total cost = $21,428.15
(a) Since, the total cost is lowest at Q = 5000 units,
Optimal order quantity = 5000 boxes
(b) Number of orders per year is calculated as,
Number of orders = Annual demand / Optimal Order Quantity
Number of orders = 15975 / 5000
Number of orders = 3.20 per year