A mail-order house uses 15,710 boxes a year. Carrying costs are 60 cents per box

Question

A mail-order house uses 15,710 boxes a year. Carrying costs are 60 cents per box a year, and ordering costs are $96. The following price schedule applies.

A mail-order house uses 15,710 boxes a year. Carrying costs are 60 cents per box a year, and ordering costs are $96. The following price schedule applies.

Determine the optimal order quantity. (Round your answer to the nearest whole number.)

Determine the number of orders per year. (Round your answer to 2 decimal places.)

A mail-order house uses 15,710 boxes a year. Carrying costs are 60 cents per box a year, and ordering costs are $96. The following price schedule applies.

Explanation / Answer

a. Optimal order quanity = [(2*annual requirement*order cost/carrying cost)]^0.5

= [(2*15710*96/0.60)]^0.50 = 2,242 boxes.

Now as per the price schedule given, the price per box for 2,242 boxes will be $1.20 per box.

Comparison of total costs for each of the order quantity should be considered. The first order level of 1,000 to 1,999 boxes has a higher price point of $1.25 and will not be considered.

Total cost = (order quantity/2)*carrying cost+(annual demand/order quantity)*ordering cost+price*annual demand

(i) scenario 1 with order quantity of 2242 boxes:

(2242/2)*0.6+(15710/2242)*96+1.2*15710 = $20,197.30

(ii) scenario 2 with order quantity of 5,000 boxes at price of $1.15:

(5000/2)*0.6+(15710/5000)*96+1.15*15710 = $19,868

(iii) scenario 3 with order quantity of 10,000 boxes at price of $1.10:

(10,000/2)*0.6+(15710/10000)*96+1.10*15710 = $20,431.80

As the price is the lowest in case of scenario 2, we should order 5,000 boxes.

b. number of orders = annual demand/optimal order quantity

= 15710/5000 = 3.14 orders.

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