Bell Computers purchases integrated chips at $350 per chip. The holding cost is
ID: 384008 • Letter: B
Question
Bell Computers purchases integrated chips at $350 per chip. The holding cost is $33 per unit per year, the ordering cost is $121 per order, and sales are steady at 395 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 $33 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).
Rich Blue Chip's Price Structure
Quantity Purchased
Price/Unit
1-99 units
$350
100-199 units
$325
200 or more units
$300
Explanation / Answer
a. Before change in price structure:
Monthly demand = 395 units
D = annual demand = 12 x 395 = 4,740 units
P = Unit cost = $350 per unit
h = holding cost per unit per year = $33
S = ordering cost = $121
Economic order quantity
To determine optimal order quantity apply continuous review model as follows:
The EOQ units = Q = (2DS/(h)) = (2*4740*121/33)
Q* = 186 units
OR EOQ = 186 units
Lot Size
Annual Purchase Cost
APC = D x P
4740 x $350
= $1,659,000
Annual Holding Cost
AHC = Q/2 x h
186/2 x $33
= $3,069
Annual Ordering
AOC = D/Q x S
4740/186 x $121
$3083.55
Total annual Cost
TC = AHC + AOC
$1,665,152.55
The optimal order quantity before the change in pricing structure is 186 units.
The total annual cost for Bell computers to order, purchase, and hold the integrated chips is $1,665,153.
b. After change in price structure and holding cost
For the given problem quantity discount or price-volume range model is applied.
Quantity Discount Model
1. For each price range (C), compute EOQ
2. If EOQ < Minimum quantity for price range, adjust the quantity to Q = Minimum for discount. If the EOQ > Maximum quantity for discount, adjust the quantity to Q = Maximum for discount. If the EOQ is within the range, then adjust Q = EOQ.
3. For each EOQ or adjusted Q, compute Total cost
4. Choose the lowest-cost quantity.
Annual Demand
A
4740.00
Ordering cost
S
121.00
Holding cost per year
I
10.00%
Quantity Range
Unit Price (P)
EOQ
order quantity
Annual Purchase Cost (APC)
Annual Ordering Cost (AOC)
Annual holding Cost (AHC)
Total Annual cost ($)
Min
Max
(2*D*S/P*I)
(Q)
D*P
(D/Q)*S
(Q/2)*(P*I)
1
99
350
181.04
(EOQ > Maximum range)
Q = 99
$1,659,000
$5,793
$1,733
$1,666,526
100
199
325
187.87
(EOQ is within range)
Q = 188
$1,540,500
$3,051
$3,055
$1,546,606
200
more
300
195.54
EOQ < Minimum range
Q = 200
$1,422,000
$2,868
$3,000
$1,427,868
The minimum total annual cost is for order quantity Q = 200, thus optimal order size is 200 units.
The optimal order quantity after the change in the holding cost calculation is 200 units.
The total annual cost for Bell computers to order, purchase, and hold the integrated chips is $1,427,868.
Lot Size
Annual Purchase Cost
APC = D x P
4740 x $350
= $1,659,000
Annual Holding Cost
AHC = Q/2 x h
186/2 x $33
= $3,069
Annual Ordering
AOC = D/Q x S
4740/186 x $121
$3083.55
Total annual Cost
TC = AHC + AOC
$1,665,152.55
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