Please complete discussion at the end by answering the 2 questions.
XYZ Corporation produces a commercial product that is in great demandby consumers on a national basis. Unfortunately, near the plant whereit is produced there is a large population of dove-tail turtles who areadversely affected by contaminants from the plant. XYZ has a filteringprocess that is expensive and any increase in filtering effectivenessreduces their profit. Dove tailed turtles are not a protected specieshence there are no environmental rules regulating XYZ’s level ofcontaminants.
Clearly, no filtering at all would maximize XYZ’sprofitability. However, a local environmental group monitors XYZ’scontaminant level and maintains a website showing the percentagemortality rate of the dove tailed turtles due to XYZ’s contaminants. XYZhas noticed that the higher the mortality percentage, the less itemsare bought and the lower their profitability.
Their MarketingDepartment and Research Group has established the following RevenueFunction, R(x), as a function of Dove Tail Turtle Mortality expressed asdecimal 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 revenuegenerated. Since XYZ has fixed operating costs of one billion dollars,the profit function, P(x) is given by P(x) = R(x) – 1.
You havebeen hired as the mathematical consultant for XYZ Corporation. They haveasked 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:
Please include the answers to questions 1 and 2 inyour discussion post.
But don’t collect your money yet. You alsounderstand that mathematics is a human activity and carries with it acertain social responsibility. Are there any ethical considerations thatyou would bring to your client’s attention?
