Target purchases home goods made by a supplier in China. Target's stores in the United States sell 200,000 units of home goods e

Question

Citrus2011

2 months ago

13

Target purchases home goods made by a supplier in China. Target's stores in the United States sell 200,000 units of home goods e

ach month. Each unit costs $10 and the company has an annual holding cost of 20 percent. Placing a replenishment order incurs clerical costs of $500/order. The shipping company charges $5,000 as a fixed cost per shipment along with a variable cost of $0.10 per unit shipped. What is the optimal order size? What is the annual holding cost of the optimal policy? How many orders per year does Target place? What is the annual variable transportation cost? What is the annual clerical cost?

Business

1 answer:

Free_Kalibri [3.7K] · Answer 1 · 2026-02-24T11:35:27+03:00

Information Provided:

Yearly Demand (D) = 200,000 × 12 = 2,400,000 units

Ordering Cost (S) = $500 each order

Carrying Cost (H) = 20% of the Unit Price = $10 × 20% = $2

Cost per Unit = $10

Calculations:

1) Optimal Order Quantity = $\sqrt{\frac{2DS}{H} }$

Optimal Order Quantity = $\sqrt{\frac{2\times 2,400,000\times 500}{2} }$

$Optimal\ Order\ Size = 34,641 Units (Approx)$

2) $Annual\ holding\ cost = (Optimal\ Order\ Size / 2) \times Holding\ Cost$

Annual Holding Expense = (34,641 / 2) × 2

Annual Holding Expense = $34,641

3) Orders Each Year = Yearly Demand / Optimal Order Quantity

Orders Each Year = 2,400,000 / 34,641

Orders Each Year = 69.2820646

Orders Each Year = 69 (Approximately)

4) Yearly Transportation Variable Cost = Cost per Unit × Yearly Demand

Yearly Transportation Variable Cost = $0.10 × 2,400,000

Yearly Transportation Variable Cost = $240,000

5) Yearly Clerical Expense = Orders Each Year × Cost Each Order

Yearly Clerical Expense = 69.282 × $500

Yearly Clerical Expense = $34,641