Question

A mail-order house uses 15,750 boxes a year. Carrying costs are 60 cents per box a year and ordering costs are $96. The following price schedule applies.

Number of Boxes	Price per Box
1,000 to 1,999	$1.25
2.000 to 4,999	1.20
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

A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $8.80 per stone for quantities of 600 stones or more, $9.50 per stone for orders of 400 to 599 stones, and $10 per stone for lesser quantities. The jewelry firm operates 184 days per year. Usage rate is 25 stones per day, and ordering costs are $48. 

a. If carrying costs are $2 per year for each stone, find the order quantity that will minimize total annual cost. (Round your intermediate calculations and final answer to the nearest whole number.) 

b. If annual carrying costs are 27 percent of unit cost, what is the optimal order size? Round your intermediate calculations and final answer to the nearest whole number.) 

c. If lead time is 7 working days, at what point should the company reorder? 

Answer 1

Answer a: EOQ = 2245 nos, as calculated below.

Annual Demand (D)	15750 nos.
Unit Order Cost (S)	$96
Holding Cost (H)	0.60 / box
Holding Cost (H)	0.6
Holding Cost (H)	$0.6
Economic Order Quantity =	Square root of [ (2 * D * S ) / (H) ]
Economic Order Quantity =	Square root of [ ( 2 * 15750 * 96 ) / (0.6) }
Economic Order Quantity =	Square root of (5040000)
Economic Order Quantity =	2244.994432 = 2245 (approx)
Economic Order Quantity =	2245 nos. ………Answer

Answer b:

7.02 nos. of optimal orders required per year to meet the demand of 15750 @ 2245 EOQ.

Optimal Number of Order Per Year =	Annual Demand / EOQ
Optimal Number of Order Per Year =	15750 / 2245
Optimal Number of Order Per Year =	7.02
Optimal Number of Order Per Year =	7.02 nos (approximate) …Answer