Question

Bell Computers purchases integrated chips at $350 per chip. The holding cost is $34 per unit per year, the ordering cost is $121 per order, and sales are steady at 400 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 annualcost?

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

(a)

Annual demand, D = 400 x 12 = 4,800
Ordering cost, K = $121
Unit holding cost, h = $34 per annum

So, EOQ without considering the discounts = (2.D.K / h)^1/2 = sqrt(2*4800*121 / 34) = 184 units

Order qty, Q	D	K	h	Unit price, C	Annual ordering cost = (D/Q)*K	Annual holding cost = (Q/2)*h	Annual puchase cost = D*C	Total cost
184	4800	121	34	325	$3,157	$3,128	$1,560,000	$1,566,285
200	4800	121	34	300	$2,904	$3,400	$1,440,000	$1,446,304

So,

The optimal order quantity after the change in pricing structure is 200

The total annual cost for Bell computers to​ order, purchase, and hold the integrated chips is $1,446,304.

(b)

Price bracket	D	K	Unit price, C	h = 10%.C	EOQ	Feasible?
<= 99	4800	121	350	35	182	No
100 - 199	4800	121	325	32.5	189	Yes
> 200	4800	121	300	30	197	No

Order qty, Q	D	K	Unit price, C	h = 10%.C	Annual ordering cost = (D/Q)*K	Annual holding cost = (Q/2)*h	Annual puchase cost = D*C	Total cost
189	4800	121	325	32.5	$3,073	$3,071	$1,560,000	$1,566,144
200	4800	121	300	30	$2,904	$3,000	$1,440,000	$1,445,904

So,

The optimal order quantity after the change in pricing structure is 200

The total annual cost for Bell computers to​ order, purchase, and hold the integrated chips is $1,445,904.

Answer 2

a) Demand (D) = 400 units per month *12 = 4800 units per year

Ordering cost (S) = $121 per order

Holding Cost (H)= $34 per unit per year

Order Size	Price (p)
1 to 99	$350
100-199	$325
200+	$300

Q(p=350) = [(2*4800*121)/(34*350)]^0.5 = 9.87

Q(p=325) = [(2*4800*121)/(34*325)]^0.5 = 10.25

Q(p=300) = [(2*4800*121)/(34*300)]^0.5 = 10.67

Optimal feasible order quantity (EOQ at p=$350)= 9.87= 10 units

Total Cost = (DS/EOQ) + (H*EOQ)/2 + (p*D)

              =((4800*121)/9.87) + ((34*350*9.87)/2) + (350*4800) = $1797571.48 = $1797572

b) Demand (D) = 400 units per month *12 = 4800 units per year

Ordering cost (S) = $121 per order

Holding Cost (H)= 10% of p per unit per year

Order Size	Price (p)
1 to 99	$350
100-199	$325
200+	$300

Q(p=350) = [(2*4800*121)/(0.1*350)]^0.5 = 182.177

Q(p=325) = [(2*4800*121)/(0.1*325)]^0.5 = 189.05

Q(p=300) = [(2*4800*121)/(0.1*300)]^0.5 = 196.77

Optimal feasible order quantity (EOQ at p=$350)= 182.177= 183 units

Total Cost = (DS/EOQ) + (H*EOQ)/2 + (p*D)

              =((4800*121)/183) + ((0.1*350*183)/2) + (350*4800) = $1686376.27 = $1686377