b) Bell Computers wishes to use a 10% holding cost rather than the fixed $34 hol
ID: 378201 • Letter: B
Question
b) Bell Computers wishes to use a 10% holding cost rather than the fixed $34 holding cost in part a. What is the optimal order quantity, and what is the optimal cost?
Bell Computers purchases integrated chips at $350 per chip. The holding cost is $33 per unit per year, the ordering cost is $123 per order, and sales are steady at 400 per month. The companys 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 1-99 units 100-199 units 200 or more units Price/Unit $350 $325 $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 isunits(enter your response as a whole number). The total annual cost for Bell computers to order, purchase, and hold the integrated chips is fround your response to the nearest whale number).Explanation / Answer
We have D (Annual demand) = 400 ´ 12 = 4800, P (Purchase price/Unit) = $350/unit, H (Holding cost /Unit) = $ 33/unit/year, S (Ordering cost/Order) = $123/order. So,
a) Q = 2DS/H
= 2 x 4,800 x 123/33
=189.16 ~ 189 units
TC = PD + HQ/2 + SD/Q
= (4800 x 325) + (33 x 189)/2 + (123 x 4,800)/189 = 1560000+3118.5+3123.8
= $1,566,242.31
However, if Bell Computers orders 200 units, which is optional with the discount model, then
TC = PD + HQ/2 + SD/Q
=4800 x 325) + (33 x 200)/2 + (123 x 4,800)/200 = 1560000+3300+2952
= $1566252
Bell Computers should order 189 units for a minimum total cost of $1,566,242.31
b)
Q = 2DS/H
= 2 x 4,800 x 123/33
= 189 units
Q = 2DS/H
= 2 x 4,800 x 123/32.5
= 191 units
Q = 2DS/H
= 2 x 4,800 x 123/30
= 198 units
189 units would not be bought at $350. 198 units cannot be bought at $300, hence that isn’t possible either. So, EOQ = 191units
TC = PD + HQ/2 + SD/Q
=(4800 x 325) + (32.5 x 191)/2 + (123 x 4,800)/191= 1560000+3103.75+ 3091.01
=$1566194.85
TC = PD + HQ/2 + SD/Q
= (4800 x 300) + (35 x 200)/2 + (123 x 4,800)/200 =1440000+3500+2772.9
= $1446452
The minimum order quantity is 200 units yet again because the overall cost of $1446452 is less than ordering 191 units, which has an overall cost of $1566194.85
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