Reference no: EM131129994
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 XYZ's level of contaminants.
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
https://www.fields.utoronto.ca/programs/mathed/meetings/minutes/12-13/HenrichSept2012.pdf
|
Determine which variables in your list are stocks
: (The Human Body and the U.S. Economy) Based on your own experiences, extend the list of analogies between the human body and the economy as outlined in this chapter. Then, determine which variables in your list are stocks and which are flows.
|
|
What percentage of the adults in the sample has an iq score
: Complete the frequency table with frequency and relative frequency. Express the relative frequency to three decimal places. What percentage of the adults in this sample has an IQ score of at least 110?
|
|
How these methods in developing your feasibility study
: Using the SCAMPER acronym, discuss at least two methods in the acronym that Tim may use to update his App to 2014? How will you use these methods in developing your feasibility study?
|
|
Balanced scorecards-customer metrics
: Many organizations focus their strategy on providing high-quality customer service and con- sequently place metrics concerning customer relationship management on their balanced scorecards. Consider Sam's Pita Pit and the Classic Steakhouse, two r..
|
|
Find the optimal dove-tail turtle mortality rate percentage
: 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.
|
|
Method to compute the economic order quantity
: Andrew and Fulton, Inc. uses 780 tons of a chemical bonding agent each year. Monthly demand fluctuates between 50 and 80 tons. The lead time for each order is one month, and the economic order quantity is 130 tons.
|
|
Parental involvement and students academic performance
: Write a thesis on the Relationship between:- "Parental Involvement and Student's Academic Performance".
|
|
Determine the magnitude of its acceleration
: The car travels up the hill with a speed of v = (0.2s) m/s where is in meters, measured from Determine the magnitude of its acceleration when it is at point s = 50 m where, r = 500 m.
|
|
Determine other main factors that account for misuse of fund
: The IMF and World Bank are the world's two leading lending institutions, but much of their monetary assistance disappears once it enters the banking systems of developing countries. Cite concrete evidence that supports the assertion that much assi..
|