位置2的问题 (Best Buy Part A) At a Best Buy store, the annual demand of a headphone is 15600. It costs $400 to place an order, the holding cost for a headphone is 10% of the unit cost, and the manufacturer charges $50 for each headphone. The unit time is one week and the manufacturer takes 2 weeks to supply an order. (Hint: Demand is not random in Part A.) (Best Buy Part A) ___ headphones should be ordered at a time.5405605806001540156015801600单项选择题
A
540
B
560
C
580
D
600
E
1540
F
1560
G
1580
H
1600

Question

位置2的问题 (Best Buy Part A) At a Best Buy store, the annual demand of a headphone is 15600. It costs $400 to place an order, the holding cost for a headphone is 10% of the unit cost, and the manufacturer charges $50 for each headphone. The unit time is one week and the manufacturer takes 2 weeks to supply an order. (Hint: Demand is not random in Part A.) (Best Buy Part A) ___ headphones should be ordered at a time.5405605806001540156015801600单项选择题

A

540

B

560

C

580

D

600

E

1540

F

1560

G

1580

H

1600

BlackTom AI · Accepted Answer

EOQ = sqrt(2DS/h), so use the economic order quantity formula.

1. Relevant concepts
- Economic Order Quantity (EOQ) minimizes total annual ordering + holding costs for deterministic demand.
- Parameters: annual demand D, ordering cost S, holding cost per unit per year h.
- Here D = 15,600 units/year, S = $400/order, unit price = $50, holding cost rate = 10% of unit cost → h = 0.10 × 50 = $5 per unit per year.

2. Step-by-step reasoning
- Apply EOQ formula: Q* = sqrt(2DS/h).
- Plug values: D = 15,600, S = 400, h = 5.

3. Calculations (showing intermediate steps)
- Compute numerator 2DS = 2 × 15,600 × 400 = (31,200) × 400 = 12,480,000.
- Divide by h: 12,480,000 / 5 = 2,496,000.
- Take square root: Q* = sqrt(2,496,000).
- sqrt(2,496,000) = sqrt(2,496 × 1,000) = sqrt(2,496) × 31.6228 ≈ 49.96 × 31.6228 ≈ 1,579.99 ≈ 1,580 units.

4. Why this answer is correct
- The EOQ calculation yields approximately 1,580 units. At this order size the annual ordering cost ≈ S·D/Q = 400·(15,600/1,580) ≈ $3,949 and annual holding cost ≈ h·Q/2 = 5·(1,580/2) = $3,950, showing the characteristic equality of holding and ordering costs at EOQ and confirming optimality.

5. Why other options are incorrect (brief)
- 600 (or similar small numbers like 540–600): these are too small to balance ordering and holding costs; note 600 equals the reorder point for a 2-week lead time (see below) but is not the EOQ.
- 1540, 1560, 1600: close but not the computed EOQ; EOQ calculation gives 1,580 (nearest option).
- Specifically, 600 = demand during lead time: weekly demand = 15,600/52 = 300; lead time 2 weeks → ROP = 300 × 2 = 600. That explains why 600 appears as an option but it answers a different quantity (reorder point), not EOQ.