Question

Bell Computers purchases integrated chips at $350 per chip. The holding cost is $37 per unit per year, the ordering cost is $122 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 annual cost? The optimal order quantity after the change in the holding cost calculation is units (enter your response as a whole number) sa (round your response to the nearest The total annual cost for Bell computers to order, purchase, and hold the integrated chips is $ whole number). dar nda

Answer 1

Solution:

Holding cost HC =37/unit

Ordering cost OC = 122/Order

Ssles =400/month

Demand D = 400*12 = 4,800

optimal order size = square root (2 * OC *D / HC)

OOS = square root (2 * 122 *4800/37)

OOS = 177.91 nos

Now we calculate the Total Cost with Order Quantity as Optimal Order Size.

1. Total cost when order quantity = optimal order size

Total cost = OC*D/OOS + HC*OOS /2 =Prce *D

= 122*4,800/178 +37*178/2+325*4,800

Total Cost =1,566,582.888

Now we calculate Total Cost with Total Cost using lowest cost of procurement.

So we consider order quantity as 200.

Total cost = OC*D/OOS + HC*OOS /2 =Prce *D

= 122*4,800/200 +37*200/2+300*4,800

Total Cost =1,446,628

The Total Cost with Order Quantity of 200 is lowest.

Total Cost is 1,446,628

Hence Proved