Answer:
Explanation:
Given that:
A mail-order house uses 18,000 boxes a year.
Carrying costs are 60 cents per box a year =$0.60
and ordering costs are $96.
Determine:
A. The optimal order quantity.
The optimal order quantity can be calculated by using the formula:
[tex]Q_o = \sqrt{\dfrac{2DS}{H}}[/tex]
[tex]Q_o = \sqrt{\dfrac{2*18000*96}{0.60}}[/tex]
[tex]Q_o = \sqrt{\dfrac{3456000}{0.60}}[/tex]
[tex]Q_o = \sqrt{5760000}[/tex]
[tex]Q_o = 2400 \ boxes[/tex]
B. The number of orders per year.
of boxes: 1,000-1,999 Price per box: $1.25
of boxes: 2,000- 4,999 Price per box: $1.20
of boxes: 5,000- 9,999 Price per box : $1.15
of boxes: 10,000 or more Price per box : $1.10
SInce 2400 boxes lies within ''of boxes: 2,000- 4,999 Price per box: $1.20 ''
Total cost = Carrying cost + ordering cost + Purchasing cost
[tex]Total \ cost =(\dfrac{Q}{2} )H +(\dfrac{D}{Q}) S+PD[/tex]
[tex]Total \ cost =(\dfrac{2400}{2} )0.60 +(\dfrac{18000}{2400}) 96+1.20*18000[/tex]
Total cost = ( 1200) 0.60 + 7.5(96) + 1.20(18000)
Total cost = 720 + 720 + 21600
Total cost = $ 23040
If the order size is 5000, the price per box will be 1.15
[tex]Total \ cost =(\dfrac{Q}{2} )H +(\dfrac{D}{Q}) S+PD[/tex]
[tex]Total \ cost =(\dfrac{5000}{2} )0.60 +(\dfrac{18000}{5000}) 96+1.15*18000[/tex]
Total cost = 2500 (0.60) + 3.6 (96) + 20700
Total cost = 1500 + 345.6 + 20700
Total cost = $22545.6
If the order size is 10000 , the price per box will be 1.10
[tex]Total \ cost =(\dfrac{Q}{2} )H +(\dfrac{D}{Q}) S+PD[/tex]
[tex]Total \ cost =(\dfrac{10000}{2} )0.60 +(\dfrac{18000}{10000}) 96+1.10*18000[/tex]
Total cost = 5000 (0.60) + 1.8(96) + 19800
Total cost = 3000 + 172.8 + 19800
Total cost = $22972.8
From the three total cost, the least minimum cost of ordering is: 5000
So; the number of orders per year = total number of boxes per year/ boxes per order
the number of orders per year = 18000/5000
the number of orders per year = 3.6 orders per year
