10. The annual demand for admission kits for patients with infectious conditions such as methicillin-resistant staphylococcus aureus (MRSA) is 2,500. The purchase price of a kit is $50. The holding cost per unit per year is 20% of the item’s price, and the cost of placing an order is $20. Demand is known and constant. If EOQ quantity is ordered every time an order is placed, how many orders per year would be placed on average?单项选择题
A
50
B
100
C
120
D
25

Question

10. The annual demand for admission kits for patients with infectious conditions such as methicillin-resistant staphylococcus aureus (MRSA) is 2,500. The purchase price of a kit is $50. The holding cost per unit per year is 20% of the item’s price, and the cost of placing an order is $20. Demand is known and constant. If EOQ quantity is ordered every time an order is placed, how many orders per year would be placed on average?单项选择题

A

50

B

100

C

120

D

25

BlackTom AI · Accepted Answer

EOQ formula sqrt(2DS/H) applies because demand is known and constant, and the goal is to balance ordering and holding costs.

1. Relevant knowledge points and concepts
- Economic Order Quantity (EOQ) minimizes total inventory cost when demand is constant and lead time is negligible.
- EOQ formula: EOQ = sqrt(2DS / H), where D = annual demand, S = ordering cost per order, H = annual holding cost per unit.
- Number of orders per year = D / EOQ.
- Holding cost H here is a percentage of unit price.

2. Complete reasoning process step by step
- Given: D = 2,500 kits/year; unit price = $50; holding cost rate = 20% of price; S = $20 per order.
- Compute H: H = 0.20 × $50 = $10 per unit per year.
- Compute EOQ: EOQ = sqrt(2 × D × S / H).

3. Calculations with intermediate steps
- 2 × D × S = 2 × 2,500 × 20 = 5,000 × 20 = 100,000.
- Divide by H: 100,000 / 10 = 10,000.
- EOQ = sqrt(10,000) = 100 units per order.
- Number of orders per year = D / EOQ = 2,500 / 100 = 25 orders/year.

4. Why the correct answer is correct
- The EOQ computation yields 100 units per order, so placing that EOQ-sized order repeatedly to meet annual demand requires 2,500/100 = 25 orders. This follows directly from the definitions and arithmetic above.

5. Why other options are incorrect
- 50: would correspond to an EOQ of 50 units (which is not supported by the formula/inputs); if EOQ were 50, orders would be 50, but the correct EOQ is 100.
- 100: is the EOQ quantity (units per order), not the number of orders per year.
- 120: does not follow from the EOQ formula or the given inputs and is arbitrary.