位置3的问题 (Demand Variations) Weekly demands of four manufacturers are:Manufacturer W: Always 30Manufacturer X: Equally likely between 20 and 40Manufacturer Y: Equally likely between 10 and 50Manufacturer Z: Equally likely between 0 and 60--- The demands of ___ are the easiest to match with supply. --- The demands of ___ are the hardest to match with supply.Manufacturer W, Manufacturer ZManufacturer X, Manufacturer YManufacturer Y, Manufacturer XManufacturer Z, Manufacturer W单项选择题
A
Manufacturer W, Manufacturer Z
B
Manufacturer X, Manufacturer Y
C
Manufacturer Y, Manufacturer X
D
Manufacturer Z, Manufacturer W

Question

位置3的问题 (Demand Variations) Weekly demands of four manufacturers are:Manufacturer W: Always 30Manufacturer X: Equally likely between 20 and 40Manufacturer Y: Equally likely between 10 and 50Manufacturer Z: Equally likely between 0 and 60--- The demands of _ are the easiest to match with supply. --- The demands of _ are the hardest to match with supply.Manufacturer W, Manufacturer ZManufacturer X, Manufacturer YManufacturer Y, Manufacturer XManufacturer Z, Manufacturer W单项选择题

A

Manufacturer W, Manufacturer Z

B

Manufacturer X, Manufacturer Y

C

Manufacturer Y, Manufacturer X

D

Manufacturer Z, Manufacturer W

BlackTom AI · Accepted Answer

Variability in demand determines how hard it is to match supply: the smaller the variability (or range/uncertainty), the easier to match supply; the larger the variability, the harder.

Relevant concepts: for a uniform (equally likely) demand between a and b, the range is b − a (a direct measure of uncertainty) and the variance is (b − a)^2 / 12 (with standard deviation = sqrt(variance)). A constant demand has zero range and zero variance, making supply matching simplest.

Step-by-step calculations for each manufacturer:
- Manufacturer W: Always 30. Range = 0 (30 − 30). Variance = 0. Standard deviation = 0.
- Manufacturer X: Equally likely between 20 and 40. Range = 40 − 20 = 20. Variance = (20)^2 / 12 = 400 / 12 = 33.333... Standard deviation = sqrt(33.333...) ≈ 5.774.
- Manufacturer Y: Equally likely between 10 and 50. Range = 50 − 10 = 40. Variance = (40)^2 / 12 = 1600 / 12 = 133.333... Standard deviation ≈ 11.547.
- Manufacturer Z: Equally likely between 0 and 60. Range = 60 − 0 = 60. Variance = (60)^2 / 12 = 3600 / 12 = 300. Standard deviation = sqrt(300) ≈ 17.321.

Ordering manufacturers by increasing uncertainty: W (0) < X (range 20, sd ≈ 5.77) < Y (range 40, sd ≈ 11.55) < Z (range 60, sd ≈ 17.32). Therefore, Manufacturer W’s demand is the easiest to match because it is constant (no uncertainty). Manufacturer Z’s demand is the hardest to match because it has the largest range and highest variance (most uncertainty).

Why other choices are wrong:
- “Manufacturer X, Manufacturer Y” suggests X is easiest and Y hardest — incorrect because X has moderate variability while W is constant and thus easiest.
- “Manufacturer Y, Manufacturer X” reverses roles incorrectly; Y has more variability than X, not less.
- “Manufacturer Z, Manufacturer W” flips easiest/hardest — Z is the most variable (hardest), not easiest.

Final confirmation: The correct answer is Manufacturer W, Manufacturer Z, matching the provided answer.

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