Question

A mail-order house uses 16,025 boxes a year. Carrying costs are 46 cents per box a year, and ordering costs are $97. The following price schedule applies. Number of Boxes Price per Box 1,000 to 1,999 $1.35 2,000 to 4,999 1.25 5,000 to 9,999 1.15 10,000 or more 1.10 Click here for the Excel Data File a. Determine the optimal order quantity. (Round your answer to the nearest whole number.) b. Determine the number of orders per year. (Round your answer to 2 decimal places.)

Answer 1

a. Optimal order quantity = 2,600 boxes

b. Number of orders per year = 6.16 orders per year

Step-by-step explanation:

a. Determine the optimal order quantity. (Round your answer to the nearest whole number.)

D = Annual demand = 16,025

O = Ordering cost = $97

C = Carrying costs = 46 cents, or $0.46

Optimal order quantity = Economic order quantity = ((2 * D * O) / C)^0.5 = ((2 * 16,025 * 97 ) / 0.46)^0.5 = 2,600 boxes

b. Determine the number of orders per year. (Round your answer to 2 decimal places.)

Number of orders per year = Annual demand / Economic order quantity = 16,025 / 2,600 = 6.16 orders per year