3 A wholesale distributor of video games has an annual demand of 12,000 X-Box Pr
ID: 365107 • Letter: 3
Question
3 A wholesale distributor of video games has an annual demand of 12,000 X-Box Prime video games. The ordering cost is $150 per order. The annual inventory carrying charge is 25%. The manufacturer provides three price breaks. An order of 1,000-4999 games has delivered price of $190 per game. Orders of 5,000 to 9,999 have a delivered price of $150 per game. Orders of 10,000 or more games are charged S130 per game. Orders under 1,000 are not accepted. a. What should the order quantity be to minimize the total annual cost of purchasing ordering, and carrying inventory? (20 points) b. At the optimal order quantity what will be the total annual cost of inventory ISpoints)Explanation / Answer
3-Demand, D=12,000 Different discounts are
S,Ordering cost=$150 per order 1- 1000-4999= $190
I= 25% of cost 2- 5000-9999= $150
H, Holding cost= I*P(Cost) 3- 10,000 and above =$130
Q=(2DS/H)
Now lets calculate Q for all discount level
Q1={(2*12,000*150)/(0.25*190)}= 3600000/47.5=275
Q2={(2*12,000*150)/(0.25*150)}= 3600000/37.5=309
Q3={(2*12,000*150)/(0.25*130)}= 3600000/32.5=333
All the values are too low to eligible, so lets adjusted upward value in each discount level
Q1=1000, Q2=5000 and Q3=10,000
Total cost in each discount level
1= 12000/1000*150+1000/2*0.25+12000*190=1800+125+2,280,000= $2,281,925
2-12000/5000*150+5000/2*0.25+12000*150=360+625+1,800,000 =$1,800,985
3-12000/10000*150+10000/2*0.25+12000*130=180+1250+1,560,000=$1,561,430
Hence total cost is minimum in 3rd discount bracket that is order of 10,000 and more in the price of $130.
b-Total annual inventory cost= 10,000/2*0.25=$1250
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