Discussion

Clearly, no filtering at all would maximize XYZ’s profitability. However, a local environmental group monitors XYZ’s contaminant level and maintains a website showing the percentage mortality rate of the dove tailed turtles due to XYZ’s contaminants. XYZ has noticed that the higher the mortality percentage, the less items are bought and the lower their profitability.

Their Marketing Department and Research Group has established the following Revenue Function, R(x), as a function of Dove Tail Turtle Mortality expressed as decimal between 0 to 1, representing mortality rate:

R(x) = 1 + x – x2; 0 < x ≤ 1

R(x) is expressed in billions of dollars and represents the revenue generated. Since XYZ has fixed operating costs of one billion dollars, the profit function, P(x) is given by P(x) = R(x) – 1.

You have been hired as the mathematical consultant for XYZ Corporation. They have asked you to help them optimize their profit and request that you:

1. Find the optimal dove-tail turtle mortality rate percentage that will maximize revenue.

2. State what the maximum profit will be.

Discussion:

As a successful mathematics student, you easily do the math and come up with the solution. Please include the answers to questions 1 and 2 in your discussion post.

But don’t collect your money yet. You also understand that mathematics is a human activity and carries with it a certain social responsibility. Are there any ethical considerations that you would bring to your client’s attention? 

References

Henrich, D. (2011, November 2). Mathematical ethics: A problem based approach. University of Toronto. Retrieved from