Question

A mail-order house uses 15,725 boxes a year. Carrying costs are 49 cents per box a year, and ordering costs are $91. 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

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

Answer 1

Annual Demand = D = 15,725 boxes

Carrying costs = H = $0.49

Ordering costs = S = $91

EOQ = = = 2,416.76 units

Hence, this EOQ is feasible for the range of 2,000 to 4,999 for a price of $1.25

Hence, the no. of units that is optimal is either EOQ or the nos. in each range nearest to EOQ. The nearest no. in each range are:

1,000 to 1,999 = 1999 for price of $1.35

2,000 to 4,999 = 2,416.76 for price of $1.25

5,000 to 9,999 = 5000 for price of $1.15

10,000 or more = 10000 for price of $1.10

We find Total cost for each of these order quantity including purchase costs:

1999 for price of $1.35:

Total Costs = Annual Ordering cost + Annual Carrying costs + Purchase Costs = = = 715.86 + 489.76 + 21,228.75‬ = $22,434.36

2,416.76 for price of $1.25:

Total Costs = Annual Ordering cost + Annual Carrying costs + Purchase Costs = = = 592.10 + 592.10 + 19,656.25‬ = $20,840.45‬

5000 for price of $1.15:

Total Costs = Annual Ordering cost + Annual Carrying costs + Purchase Costs = = = 286.19 + 1,225‬ + 18,083.75‬‬ = $19,594.94‬

10000 for price of $1.10​​​​​​​:

Total Costs = Annual Ordering cost + Annual Carrying costs + Purchase Costs = = = 143.10 + 2,450‬‬ + 17,297.5‬‬‬ = $19,890.6‬

As seen from above, the value of total cost is least for 5000 units at $19,594.94

Hence, Optimal order quantity = 5000 units

Number of order = D / Q = 15725 / 5000 = 3.15 orders

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