his week, we have a pretty detailed topic, so expect to spend a little extra time working on the discussion this week. As always, feel free to explore this topic more deeply through the conversation.
Again, like we have been doing, at the end of the discussion, you will be asked to craft a 150 word reflection on what you have learned through this conversation and post it to the Reflection Journal. Dive in, be active, help out your classmates when they need it, and, because we could never say this enough, enjoy the conversation.
XYZ Corporation produces a commercial product that is in great demand by consumers on a national basis. Unfortunately, near the plant where it is produced there is a large population of dove-tail turtles who are adversely affected by contaminants from the plant. XYZ has a filtering process that is expensive and any increase in filtering effectiveness reduces their profit. Dove tailed turtles are not a protected species hence there are no environmental rules regulating XYZâ€™s level of contaminants.
Clearly, no filtering at all would maximize XYZâ€™s profitability. However, a local environmental group monitors XYZâ€™s contaminant level and maintains a website showing the percentage mortality rate of the dove tailed turtles due to XYZâ€™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 â€“ x2; 0 < x â‰¤ 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) â€“ 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.
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 donâ€™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 clientâ€™s attention?