Question

In: Operations Management

A mail-order house uses 15,725 boxes a year. Carrying costs are 49 cents per box a...

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

Expert Solution

a) Optimal order quantity 5000 boxes

The standard EOQ equation is given as below

where D is the annual demand, K is the ordering cost and h is the carrying cost.

Hence without the price discount, we have the EOQ as below

To determine the optimal order quantity, we need to compare the total cost of ordering 2417 with total cost of ordering 5000 and 10000. Total cost is the sum of ordering cost, carrying cost and purchase cost.

Total Ordering cost = (Annual Demand)/(Order Quantity)*(Ordering Cost)

Total Carrying cost = (Order Quantity)/2*(Carrying cost)

Total Purchase cost = (Annual Price)*(Purchase Cost)

For quantity = 2417

Total Ordering cost = (15725)/(2417)*(91) = 592.05

Total Carrying cost = (2417)/2*(0.49) = 592.17

Total Purchase cost = (15725)*(1.25) = 19656.25

Total cost = 592.05+592.17+19656.25 = 20840.47

For quantity = 5000

Total Ordering cost = (15725)/(5000)*(91) = 286.20

Total Carrying cost = (5000)/2*(0.49) = 1225

Total Purchase cost = (15725)*(1.15) = 18083.75

Total cost = 286.20+1225+18083.75 = 19594.95

For quantity = 10000

Total Ordering cost = (15725)/(10000)*(91) = 143.1

Total Carrying cost = (10000)/2*(0.49) = 2450

Total Purchase cost = (15725)*(1.1) = 17297.5

Total cost = 143.1+2450+17297.5 = 19890.6

We can see that the option with ordering 5000 quantity has the lowest cost. Hence optimal order quantity is 5000.

b) Number of order 3.15 per year

Number of orders is calculated by dividing the annual demand by the order quantity. In this case the annual demand is 15725 and the order quantity is 5000. Hence the number of orders per year are 15725/5000 = 3.15

keosha answered 1 month ago

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