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MMLU-Pro / 808 / A gas main carrying natural gas and laid in a corrosive soil ultimately reaches…

Problem

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question

A gas main carrying natural gas and laid in a corrosive soil ultimately reaches the point where it develops small leaks that increase as time goes on. Assume the cost per mile of main is 8,000,thatnogasislostforthefirst15yearsoflife,andthatamainhaszeronetsalvagevaluewheneverretired.Assumealsothatthemileofmainloses8,000, that no gas is lost for the first 15 years of life, and that a main has zero net salvage value whenever retired. Assume also that the mile of main loses 60 worth of gas in the 16th year of life and that the cost of lost gas increases $60 every year thereafter. Interest or minimum attractive return is at 7%. Compare the equivalent uniform annual cost over the life of a main retired after 20 years with the equivalent uniform annual cost over the life of the main retired after 25 years.
Plain-text mathematical notation (without MathML)
A gas main carrying natural gas and laid in a corrosive soil ultimately reaches the point where it develops small leaks that increase as time goes on. Assume the cost per mile of main is 8,000,thatnogasislostforthefirst15yearsoflife,andthatamainhaszeronetsalvagevaluewheneverretired.Assumealsothatthemileofmainloses60 worth of gas in the 16th year of life and that the cost of lost gas increases $60 every year thereafter. Interest or minimum attractive return is at 7%. Compare the equivalent uniform annual cost over the life of a main retired after 20 years with the equivalent uniform annual cost over the life of the main retired after 25 years.
Original LaTeX notation
A gas main carrying natural gas and laid in a corrosive soil ultimately reaches the point where it develops small leaks that increase as time goes on. Assume the cost per mile of main is $8,000, that no gas is lost for the first 15 years of life, and that a main has zero net salvage value whenever retired. Assume also that the mile of main loses $60 worth of gas in the 16th year of life and that the cost of lost gas increases $60 every year thereafter. Interest or minimum attractive return is at 7%. Compare the equivalent uniform annual cost over the life of a main retired after 20 years with the equivalent uniform annual cost over the life of the main retired after 25 years.

category

business

options

  1. The total annual cost of the 25-year line is substantially lower than that of the 20-year line due to reduced leak repair costs
  2. The total annual cost of the 20-year line is equal to that of the 25-year line when including the cost of gas loss
  3. The total annual cost of the 25-year line is equal to that of the 20-year line
  4. The total annual cost of the 20-year line is lower than that of the 25-year line when factoring in technological improvements in leak detection
  5. The total annual cost of the 20-year line is lower than that of the 25-year line
  6. The total annual cost of the 25-year line is higher than that of the 20-year line due to higher cumulative gas loss
  7. The total annual cost of the 25-year line is lower than that of the 20-year line
  8. The total annual cost of the 20-year line is higher than that of the 25-year line due to increased maintenance costs
  9. The total annual cost of the 25-year line is higher than that of the 20-year line
  10. The total annual cost of the 25-year line is slightly higher than that of the 20-year line due to escalating gas prices

src

stemez-Business

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Source and history

upstream_id / Original problem ID
808
task_id
9486f9df-3dc2-5db5-a76f-6451f73a2aca
task_key
default--test--808
task_revision_id
1
config / split
default / test

Official source

initial import