QUESTION 12 Copy of Mac-in-the-Box Inc. is a computer store that sells computer
ID: 383306 • Letter: Q
Question
QUESTION 12 Copy of Mac-in-the-Box Inc. is a computer store that sells computer equipment. The store is open for 50 weeks in a year. Sales of a popular laptop model are 1000 per year. Ordering cost is $300, and annual holding cost is 20%. The store buys the laptop from a suppleir that offers the following price structure: Ordering quantity Price ($) per unit 0 to 24550 25 to 124 470 125or more 400 What is the optimal ordering quantity? (Ordering quantity must be rounded to the nearest integer as fractions of a laptop can not be ordered.) Show all major steps to get full marks. As part of your answer also provide the total annual cost (holding and ordering cost,) associated with the optimal ordering quantity Please upload a file containing your answer. You can solve the question on a piece ofpaper by hand and upload a legible picture, or solve it in Word and upload a Word document Attach File Browse My Computer Browse Content Collection Browse DropboxExplanation / Answer
Annual demand (D) = 1000 per year
Ordering cost (S) = $300
Holding cost (H) = 20% of price
Order quantity price Holding cost
0-24 550 $110(as 20% of $550)
25-124 470 $94(as 20% of $470)
125 or more 400 $80(as 20% of $400)
Now we have to find the minimum point for each price starting with the lowest price until the feasible minimum point is located.
Minimum point for price of $400 = sqrt of (2DS /H)
= sqrt of [(2 x 1000 x 300)/80]
= sqrt of 7500
= 86.60 or rounded to 87
Because an order size of 87 will cost $470 instead of $400 it is not a minimum feasible point for price of $400.
Next we try for price of $470. The minimum point for price of $470 = sqrt of(2DS /H)
= sqrt of [(2 x 1000 x 300) / 94]
= 79.89 or rounded to 80
As the order size of 80 will cost $470 per unit, it is a feasible point for price of $470
Now we have to calculate the total cost for the order size of 80 and compare it with the total cost of the minimum quantity needed to obtain a price of $400.The price of $550 will not be considered as it is higher than the price of the feasible point.
with order quantity (Q) = 80 units,
Total cost = Ordering cost + Holding cost
= [(D / Q) S] + [(Q /2)H]
= [(1000/80)300] + [(80/2)94]
= $3750 + $3760
= $7510
To obtain an unit price of $400, the minimum order quantity needed is 125 units. So with order quantity (Q) = 125 units the Total cost = Ordering cost + Holding cost
= [(D /Q) S] + [(Q /2)H]
= [(1000/125)300] + [(125/2)80]
= $2400 + $5000
= $7400
So the optimal order quantity is 125 laptops as it has the lowest total cost.
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