位置5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) (Note: To avoid rounding errors, use exactly the same order quantity in a previous question.) --- Total setup cost is ___. --- Total holding cost is ___.3919.37, 39203929.37, 39303939.37, 39403949.37, 39503919.37, 67503929.37, 67603939.37, 67703949.37, 6780Single choice
A
3919.37, 3920
B
3929.37, 3930
C
3939.37, 3940
D
3949.37, 3950
E
3919.37, 6750
F
3929.37, 6760
G
3939.37, 6770
H
3949.37, 6780

Question

位置5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) (Note: To avoid rounding errors, use exactly the same order quantity in a previous question.) --- Total setup cost is _. --- Total holding cost is _.3919.37, 39203929.37, 39303939.37, 39403949.37, 39503919.37, 67503929.37, 67603939.37, 67703949.37, 6780Single choice

A

3919.37, 3920

B

3929.37, 3930

C

3939.37, 3940

D

3949.37, 3950

E

3919.37, 6750

F

3929.37, 6760

G

3939.37, 6770

H

3949.37, 6780

BlackTom AI · Accepted Answer

EOQ formula gives Q* = sqrt(2DS/H). Here D = 15,600 units/year, S = $400 per order, unit cost = $50 so annual holding cost per unit H = 10% × $50 = $5/year.

1) Relevant knowledge points and concepts
- Economic Order Quantity (EOQ): Q* = sqrt(2DS/H).
- Annual setup (ordering) cost = (D/Q) × S.
- Annual holding cost = (Q/2) × H.
- For deterministic demand, reorder point and lead time are separate; EOQ determines Q.

2) Step-by-step reasoning
- Compute H = 0.10 × 50 = $5 per unit per year.
- Compute the EOQ: Q* = sqrt(2 × D × S / H).

3) Calculations (all intermediate steps)
- 2 × D × S = 2 × 15,600 × 400 = 31,200 × 400 = 12,480,000.
- Divide by H: 12,480,000 / 5 = 2,496,000.
- Q* = sqrt(2,496,000) ≈ 1,579.87 units. Using the instruction to use the same order quantity as the previous question and rounding to whole units gives Q = 1,580 units.
- Number of orders per year = D / Q = 15,600 / 1,580 ≈ 9.8734177215 orders/year.
- Total setup (ordering) cost = (D/Q) × S = 9.8734177215 × $400 ≈ $3,949.3670886 → $3,949.37 (rounded to cents).
- Average inventory = Q/2 = 1,580 / 2 = 790 units.
- Total holding cost = (Q/2) × H = 790 × $5 = $3,950.00.

4) Why the correct answer is correct
The pair (3,949.37, 3,950.00) directly follows from the EOQ-calculated order quantity of 1,580 units and the standard formulas for annual ordering and holding costs. Ordering cost uses the number of orders times $400; holding cost uses average inventory times $5 per unit-year.

5) Why other options are incorrect
All other answer pairs do not match the values produced by the EOQ rounding to Q = 1,580 and the exact arithmetic above (they give different setup or holding cost values that are inconsistent with D, S, H and Q = 1,580).

6) Conclusion / confirmation
Therefore the total setup cost is $3,949.37 and the total holding cost is $3,950.00, which matches the provided answer: 3949.37, 3950.