A mail-order house uses 15,320 boxes a year. Carrying costs are 60 cents per box

Question

A mail-order house uses 15,320 boxes a year. Carrying costs are 60 cents per box a year, and ordering costs are $96. The following price schedule applies, ? Number of Boxe 111 . Price per Box:11111 1,000 to 1,999 2,000 to 4,999 5,000 to 9,999 10,000 or more $1.25 1.20 1.15 1.10 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 order per year eBook & Resources

Explanation / Answer

Demand (D) = 15,320

Ordering cost (S) = 96 $

Carrying cost (H) = 0.6 $

Optimal order quantity (EOQ) = sqrt(2*D*S/H) = sqrt(2*15320*96/0.6) = 2214

Total cost = D/EOQ*S + EOQ/2*H + Price*D

1) EOQ = 2214, Price = 1.2

Total cost = 15320/2214*96 + 2214/2*0.6 + 1.2*15320 = 19712

2) EOQ = 5000, Price = 1.15

Total cost = 15320/5000*96 + 5000/2*0.6 + 1.15*15320 = 19412

3) EOQ = 10000, Price = 1.1

Total cost = 15320/10000*96 + 10000/2*0.6 + 1.1*15320 = 19999

a) Optimal is Case 2 = 5000 boxes

b) Number of orders = D/EOQ = 15320/5000 = 3.06

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