Mathematics

Utility Company Cost Function

You work for a utility company that burns coal to generate electricity. The cost C (in dollars) of removing p (percent, no need to change to a decimal) amount of the smokestack pollutants is given by:

LaTeX: C=frac{100,000p}{100-p}

C=100,000p100p

  1. Graph the cost function. Use a scale of 10 units per grid point on the p-axis and 100,000 units on the C-axis. What is the domain for this problem? Why? (3 points)
  2. Government regulations require you to remove at least 70% of the pollutants. What would be the cost of meeting this requirement? Round to the nearest cent. (3 points)
  3. Psychologists from your marketing department recommend exceeding the government mandate by 15% to improve public opinion of the company. What would the cost of meeting this requirement be? Round to the nearest cent. (3 points)
  4. The CFO of your company has allocated $1,000,000 to reducing smokestack pollutants. What percent of the pollutants could you remove with this budget? Round to the nearest tenth of a percent. (3 points)
  5. An environmentally conscious and influential politician in California is calling for the power industry to remove 100% of the pollutants from coal based power plants. Your lobbyists want to know how to address this issue with politicians before things get out of hand. How would you educate your lobbyists to respond to this politician? You should include some math in your explanation, but be sure to explain what is going on. It is important to describe the costs as the percentage gets very close to 100% as well as considering what happens if p = 100. (4 points)

The points for each part include points for your explanations and justifications of each part.

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