Question

Bell Computers purchases integrated chips at $350.00 per chip. The holding cost is $35.00 per unit per year, the ordering cost is $120.00 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 pric 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 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 S (round your response to the nearest whole number). b) Bell Computers wishes to use a 10% holding cost rather than the fixed $35.00 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

ANSWER:

Given that,

a)

Optimal order quantity EOQ = SQRT(2*D*S/H) = SQRT(2*4800*120/35) = 181 units (approx)

Minimum/Total cost = Holding cost+Purchasing cost+Ordering cost

Total cost = (Q/2)*H + p*Q + (D/Q)*S

As the EOQ is 181 -- in the range of 100-199 units, the purchasing cost/unit (p) = 325 $/unit

Total cost = (181/2)*35 + 4800*325 + (4800/181)*120 = 1,566,350​ $ (approx)

b)

H₁ = 10%*350 = 35 $ (1-99 units)

H₂ = 10%*325 = 32.5 $ (100-199 units)

H₃ = 10%*300 = 30 $ (200+ units)

Optimal order quantity Q₁= SQRT(2*D*S/H₁) = 181 units (from a)

Q₂ = SQRT(2*D*S/H₂) = SQRT(2*4800*120/32.5) = 188 units (approx)

Q₃ = SQRT(2*D*S/H₃) = SQRT(2*4800*120/30) = 196 units (approx)

The only possible value for EOQ = 188 units

Total cost = (Q/2)*H + p*Q + (D/Q)*S

Total cost = (188/2)*32.5 + 325*4800 + (4800/188)*120 = 1566120 $ (approx)