Problem 13-13 A mail-order house uses 15,775 boxes a year. Carrying costs are 68
ID: 332416 • Letter: P
Question
Problem 13-13 A mail-order house uses 15,775 boxes a year. Carrying costs are 68 cents per box a year, and ordering costs are $93. 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 quantityboxes b. Determine the number of orders per year. (Round your answer to 2 decimal places.) Number of order per yearExplanation / Answer
Given values:
Annual demand, D = 15,775 boxes per year
Carrying costs, Cc = 68 cents per box a year = $0.68
Ordering cost, Co = $93
Purchase price:
(1,000 = < Q = < 1,999), P = $1.45 per box
(2,000 = < Q = < 4,999), P = $1.35 per box
(5,000 = < Q = < 9,999), P = $1.25 per box
(10,000 = < Q), P = $1.20 per box
Solution:
(a) Optimal order quantity or Economic order quantity can be calculated as;
EOQ = SQRT [(2*D*Co) / Cc]
where,
D = Annual demand
Co = Ordering costs
Cc = Carrying costs
EOQ = SQRT [(2 x 15775 x 93) / 0.68]
EOQ = SQRT (4314926.471)
EOQ = 2077.24 or 2077
Optimal order quantity = 2077 boxes
(b) Number of orders per year can be calculated as;
Number of orders = Annual demand / Optimal order quantity
Number of orders = 15775 / 2077
Number of orders = 7.60 per year