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Difficulty: MediumIntegrated Table and Graphical Analysis

A fintech corporation tracks server performance metrics across five regional data centers: Region Alpha, Region Beta, Region Gamma, Region Delta, and Region Epsilon.

The table below presents Q3 transaction processing latency and cluster allocations:

Data CenterAverage Transaction Latency (ms)Active Server Clusters
Region Alpha12015
Region Beta8510
Region Gamma15020
Region Delta9512
Region Epsilon11014
Additionally, graphical analysis indicates that monthly operational expenses (yy, in thousands of dollars) correlate linearly with active server clusters (xx) according to the line of best fit y=4.5x+10y = 4.5x + 10.

Which of the following correctly pairs the data center with the lowest latency per active server cluster and its predicted monthly operational expense (in thousands of dollars)?

  1. Region Gamma; $100 thousandAnswer
  2. B
    Region Beta; $55 thousand
  3. C
    Region Gamma; $90 thousand
  4. D
    Region Alpha; $77.5 thousand
  5. E
    Region Delta; $64 thousand

Answer

Region Gamma; $100 thousand
Evaluating the latency per active server cluster for each data center yields 8.08.0 ms for Region Alpha, 8.58.5 ms for Region Beta, 7.57.5 ms for Region Gamma, 7.927.92 ms for Region Delta, and 7.867.86 ms for Region Epsilon. Region Gamma exhibits the lowest rate (7.57.5 ms per cluster). Applying its 2020 active server clusters to the graphical trend line y=4.5x+10y = 4.5x + 10 gives y=4.5(20)+10=100y = 4.5(20) + 10 = 100 thousand dollars.

Step-by-Step Solution

1
Calculate the latency per active server cluster for each data center using table data.
Region Alpha: 120/15=8.0120 / 15 = 8.0 ms/cluster; Region Beta: 85/10=8.585 / 10 = 8.5 ms/cluster; Region Gamma: 150/20=7.5150 / 20 = 7.5 ms/cluster; Region Delta: 95/12≈7.9295 / 12 \approx 7.92 ms/cluster; Region Epsilon: 110/14≈7.86110 / 14 \approx 7.86 ms/cluster.
Dividing latency by active server clusters isolates efficiency per unit cluster.
2
Identify the data center with the minimum ratio.
Region Gamma has the lowest latency per active server cluster at 7.57.5 ms/cluster.
Comparing calculated rates reveals the minimum value.
3
Use the linear model equation y=4.5x+10y = 4.5x + 10 to find the operational expense for Region Gamma.
Substitute x=20x = 20 active server clusters into the trend equation: y=4.5(20)+10=90+10=100y = 4.5(20) + 10 = 90 + 10 = 100.
Region Gamma operates 2020 active server clusters.

Key Concept

Integrated Table and Graphical Analysis
Estimated Time:2m 0s
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Topics

Integrated Table and Graphical Analysis