Question

A mail-order house uses 15,750 boxes a year. Carrying costs are 45 cents per box a year, and ordering costs are $92. 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

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   

Answer 1

Given:

Annual Demand =15,750 per year

Ordering cost = 0.45$ per order

Holding cost = 92$

Q= Optimal Order Quantity

= sqrt[ ( 2 * Annual Demand * holding cost)/ordering cost

]

a. Determine the optimal order quantity

Q1_{0,000 or more} = sqrt [(2*15750*92)/0.45*1.15] = 2367

this EOQ is not feasible as 2367 is less than 10,000

Q_{5,000 to 9,999?} = sqrt [(2*15750*92)/0.45*1.20] = 2317

this is also not feasible as 2317 is less than 5000

Q_{2,000 to 4,999?} = sqrt [(2*15750*92)/0.45*1.30] = 2226

this is feasible because 2226 is less than 4999 and more than 2000

Now we need to compare total cost of 2226 with that of 5000 & 10000 boxes to find best Q:

Total Cost₂₂₂₆ = 2226/2 * (0.60)(1.30) + 15,750/2226 * (92) +1.30(15750)

868.14+650.94+20475= 21994.08

Total Cost₅₀₀₀ = 5000/2 * (0.60)(1.20) + 15,750/5000 * (92) +1.20(15750)

1800 + 289.8 +18,900 = 20,989.8

Total Cost_10,000 = 10,000/2 * (0.60)(1.15) + 15,750/10,000 * (92) +1.15(15750)

3450 +144.9 +18112.5 = 21,707.4

We can see here that Total Cost₅₀₀₀ is the lowest = 20,989.8 hence best order quantity will be 5000

b. Determine the number of orders per year

= Demand/Quantity = 15750/5000= 3.15 orders per year