Thaarugo, inc., produces a GPS device that is becoming popular in parts of scandinavia, When thaarugo produces one of these, a printed circuit board (PCB) is used, and it is populated with several electronic components, Thaarugo determines that it needs about 16,000 of this type of PCB each year. Demand is relatively constant throughout the year, and the ordering cost is about $25 per order; the holding cost is 20% of the price of each PCB. Two companies are competing to become the dominant supplier of the PCBs, and both have now offered discounts, as shown in the followinf table. which of the two suppliers should be selected if Thaarugo wishes to minimize total annual inventory cost? What would be the annual inventory cost?


supplier A Supplier B
Quantity Price Quantity Price
1-199 38.40 1-299 39.50
200-499 35.80 300-999 35.40
500 or more 34.70 1000 ormore 34.60

Thaarugo, inc., produces a GPS device that is becoming popular in parts of scandinavia, When thaarugo produces one of these, a printed circuit board (PCB) is used, and it is populated with several electronic components, Thaarugo determines that it needs about 16,000 of this type of PCB each year. Demand is relatively constant throughout the year, and the ordering cost is about $25 per order; the holding cost is 20% of the price of each PCB. Two companies are competing to become the dominant supplier of the PCBs, and both have now offered discounts, as shown in the followinf table. which of the two suppliers should be selected if Thaarugo wishes to minimize total annual inventory cost? What would be the annual inventory cost?

supplier A Supplier B
Quantity Price Quantity Price
1-199 38.40 1-299 39.50
200-499 35.80 300-999 35.40
500 or more 34.70 1000 ormore 34.60

To determine which supplier should be selected to minimize total annual inventory cost, we need to calculate the annual inventory cost for each supplier.

For Supplier A:
- If the quantity needed is less than 200, the price per PCB is $38.40.
- If the quantity needed is between 200 and 499, the price per PCB is $35.80.
- If the quantity needed is 500 or more, the price per PCB is $34.70.

For Supplier B:
- If the quantity needed is less than 300, the price per PCB is $39.50.
- If the quantity needed is between 300 and 999, the price per PCB is $35.40.
- If the quantity needed is 1000 or more, the price per PCB is $34.60.

To calculate the annual inventory cost, we need to consider the ordering cost and the holding cost.

Step 1: Calculate the optimal order quantity for each supplier.
We can use the Economic Order Quantity (EOQ) formula to calculate the optimal order quantity:
EOQ = √((2DS) / H)
Where:
D = Annual demand (16,000 PCBs)
S = Ordering cost ($25 per order)
H = Holding cost (20% of the price per PCB)

For Supplier A:
EOQ_A = √((2 * 16,000 * 25) / (0.2 * 38.40))

For Supplier B:
EOQ_B = √((2 * 16,000 * 25) / (0.2 * 39.50))

Step 2: Calculate the annual inventory cost for each supplier using the optimal order quantity calculated.
Annual Inventory Cost_A = D * (P_A + (EOQ_A / 2) * H_A)
Annual Inventory Cost_B = D * (P_B + (EOQ_B / 2) * H_B)
Where:
P_A = Price per PCB for Supplier A
P_B = Price per PCB for Supplier B
H_A = Holding cost for Supplier A
H_B = Holding cost for Supplier B

Calculate the EOQ and annual inventory cost for Supplier A:
EOQ_A = √((2 * 16,000 * 25) / (0.2 * 38.40)) ≈ 375.84 PCBs
Annual Inventory Cost_A = 16,000 * (P_A + (375.84 / 2) * H_A)

Next, calculate the EOQ and annual inventory cost for Supplier B:
EOQ_B = √((2 * 16,000 * 25) / (0.2 * 39.50)) ≈ 381.46 PCBs
Annual Inventory Cost_B = 16,000 * (P_B + (381.46 / 2) * H_B)

To determine which supplier has the minimum annual inventory cost, compare the calculated costs for Supplier A and Supplier B.

Once we have the prices and holding costs for Supplier A and Supplier B, the calculations can be completed to determine the annual inventory cost for each supplier.

To determine which supplier should be selected to minimize the total annual inventory cost, we need to consider the ordering cost, holding cost, and the price of each PCB.

1. Calculate the annual demand for Thaarugo's GPS device:
Annual demand = 16,000 PCBs

2. Calculate the EOQ (Economic Order Quantity) for each supplier:
EOQ = √(2DS/H)
where D is the annual demand, S is the ordering cost, and H is the holding cost per unit.

For Supplier A:
EOQ_A = √(2 * 16,000 * $25 / (0.2 * $38.40))

For Supplier B:
EOQ_B = √(2 * 16,000 * $25 / (0.2 * $39.50))

3. Check which price bracket fits the EOQ for each supplier:
For Supplier A:
EOQ_A falls under the price bracket 200-499, so the price per PCB is $35.80.

For Supplier B:
EOQ_B falls under the price bracket 300-999, so the price per PCB is $35.40.

4. Calculate the total annual inventory cost for each supplier:
Total Cost_A = (D / EOQ_A) * S + (EOQ_A / 2) * H * $35.80
Total Cost_B = (D / EOQ_B) * S + (EOQ_B / 2) * H * $35.40

Plug in the values:
Total Cost_A = (16,000 / EOQ_A) * $25 + (EOQ_A / 2) * 0.2 * $35.80
Total Cost_B = (16,000 / EOQ_B) * $25 + (EOQ_B / 2) * 0.2 * $35.40

5. Compare the total annual inventory costs for each supplier:
If Total Cost_A < Total Cost_B, choose Supplier A.
If Total Cost_B < Total Cost_A, choose Supplier B.

The supplier with the lower total annual inventory cost would be the one selected to minimize costs for Thaarugo.

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