Question

A mail-order house uses 18,000 boxes a year. Carrying costs are 60 cents per box a year, and ordering costs are $96. The following price schedule applies.
Determine:
A. The optimal order quantity.
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

Answer 1

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:

$Q_o = \sqrt{\dfrac{2DS}{H}}$

$Q_o = \sqrt{\dfrac{2*18000*96}{0.60}}$

$Q_o = \sqrt{\dfrac{3456000}{0.60}}$

$Q_o = \sqrt{5760000}$

$Q_o = 2400 \ boxes$

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

$Total \ cost =(\dfrac{Q}{2} )H +(\dfrac{D}{Q}) S+PD$

$Total \ cost =(\dfrac{2400}{2} )0.60 +(\dfrac{18000}{2400}) 96+1.20*18000$

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

$Total \ cost =(\dfrac{Q}{2} )H +(\dfrac{D}{Q}) S+PD$

$Total \ cost =(\dfrac{5000}{2} )0.60 +(\dfrac{18000}{5000}) 96+1.15*18000$

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

$Total \ cost =(\dfrac{Q}{2} )H +(\dfrac{D}{Q}) S+PD$

$Total \ cost =(\dfrac{10000}{2} )0.60 +(\dfrac{18000}{10000}) 96+1.10*18000$

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