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) = 15725 units

ordering cost(S) = $91

Holding cost(H) = 49 cents = $0.49

For this problem we have to first calculate the common Economic order Quantity as the holding cost for all range is the same.So the common EOQ = sqrt of (2DS/H)

= √[(2X15725X91) / 0.49]

= √(2861950/0.49)

= √5840714.2857

= 2417 units

We can order 2417 units at a price of $1.25

Total cost with order quantity(Q) of 2417 units = [(Q/2)/H] + [(D/Q)S] + (Price X D)

= [(2417/2)0.49] + [(15725/2417)91] + (1.25 X 15725)

= $592.17 + $592.05 + $19656.25

= $20840.47

Because lower price ranges exist each must be checked against the cost generated by 2417 units at the price of $1.25

The minimum units required to order to obtain a price of $1.15 is 5000 units.So the total cost with an order quantity(Q) of 5000 units = [(Q/2)H] + [(D/Q)S] + (Price X D)

= [(5000/2)0.49] + [(15725/5000)91] + (1.15 X 15725)

= $1225 + $286.20 + $18083.75

= $19594.95

The minimum units required to order to obtain a price of $1.10 is 10000 units.So the total cost with an order quantity(Q) of 10000 units = [(Q/2)H] + [(D/Q)S] + (Price X D)

= [(10000/2)0.49] + [(15725/10000)91] + (1.10 X 15725)

= $2450 + $143.10 + $17297.5

= $19890.60

So the optimal order quantity is 5000 boxes as it has the lowest total cost of $19594.95

b) Number of orders per year = D/Economic Order Quantity = 15725/5000 = 3.15