Question

Bell Computers purchases integrated chips at $350 per chip. The holding cost is $37 per unit per year, the ordering cost is $123 per order, and sales are steady at 405 per month. The company's supplier, Rich Blue Chip Manufacturing, Inc., decides to offer price concessions in order to attract larger orders. The price structure is shown below. 

Rich Blue Chip's Price Structure 

Quantity Purchased	Price/Unit
1-99 units	$350
100-199 units	$325
200 or more units	$300

a) What is the optimal order quantity and the minimum annual cost for Bell Computers to order, purchase, and hold these integrated chips? 

The optimal order quantity after the change in pricing structure is units (enter your response as a whole number). 

The total annual cost for Bell computers to order, purchase, and hold the integrated chips is $ (round your response to the nearest whole number). 

b) Bell Computers wishes to use a 10% holding cost rather than the fixed $37 holding cost in part a. What is the optimal order quantity, and what is the optimal annual cost? 

The optimal order quantity after the change in the holding cost calculation is units (enter your response as a whole number). 

The total annual cost for Bell computers to order, purchase, and hold the integrated chips is $ (round your response to the nearest whole number).

Answer 1

Considering the following values:

Annual Demand (405 x 12)	4,860 per year
Holding Cost (H)	$ 37 per year
Ordering Cost (S)	$ 123 per order
Purchase cost	$ 350 per chip

(a) Initially determine the Optimal Order Quantity (EOQ) as below:

Now, determine the minimum cost for the Bell Company to order:

Quantity Ordered (Q)	Order Cost	Purchasing Cost	Holding Cost	Total Cost
(A)	(B) = (4,860 / A x 123)	(C) = (4,860 x Price)	(D) = (A / 2) x 37	(A) + (B) + (C) + (D)
180	3,321	1,579,500	3,330.00	1,586,151.00
99	6,038.1818	1,701,000	1,831.50	1,708,869.68
199	3,003.9196	1,579,500	3,681.50	1,586,185.42
200	2,989.9	1,458,000	3,700.00	1,464,689.90

Hence the optimal Order Quantity for Bell Computers is 200 units. The minimum cost to order , purchase, and hold these integrated chips is $1,464,689.90.

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(b) Bell Computers wishes to use a 10% holding cost rather than fixed holding cost. Determine the Optimal order quantity and optimal cost as beloe:

In this case, holding cost will be calculated using the given formula:

Quantity Ordered (Q)	Order Cost	Purchasing Cost	Holding Cost	Total Cost
(A)	(B) = (4,860 / A x 123)	(C) = (4,860 x Price)	(D) = (A / 2) x (0.10 x Price)	(A) + (B) + (C) + (D)
180	3,321	1,579,500	2,925.00	1,585,746.00
99	6,038.1818	1,701,000	1,732.50	1,708,770.68
199	3,003.9196	1,579,500	3,233.75	1,585,737.67
200	2,989.9	1,458,000	3,000.00	1,463,989.90

Hence the optimal Order Quantity for Bell Computers is 200 units. The minimum cost to order , purchase, and hold these integrated chips is $1,463,989.90.