Question

A mail-order house uses 15,950 boxes a year. Carrying costs are 69 cents per box a year, and ordering costs are $100. The following price schedule applies.

Number of Boxes		Price per Box
1,000 to 1,999		$1.40
2,000 to 4,999		1.30
5,000 to 9,999		1.20
10,000 or more		1.15

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

Annual demand(D) = 15950 units

ordering cost(S) = $100

Holding cost(H) = 69 cents = $0.69

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)

= Sqrt of [(2X15950X100) / 0.69]

= 2150 units

We can order 2150 units at a price of $1.30

Total cost with order quantity(Q) of 2150 units = [(Q/2)/H] + [(D/Q)S] + (Price X D)

= [(2150/2)0.69] + [(15950/2150)100] + (1.30 X 15950)

= $741.75 + $741. 86 + $20735

= $22218.61

Because lower price ranges exist each must be checked against the cost generated by 2150 units at the price of $1.30

The minimum units required to order to obtain a price of $1.20 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)0.69] + [(15950/5000)100] + (1.20 X 15950)

= $1725 + $319 + $19140

= $21184

The minimum units required to order to obtain a price of $1.15 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)0.69] + [(15950/10000)100] + (1.15 X 15950)

= $3450 + $159. 5 + $18342.5

= $21952

So the optimal order quantity is 5000 boxes as it has the lowest total cost of $21184

b) Number of orders per year = D/Economic Order Quantity = 15950/5000 = 3.19