# Xyz | Mathematics homework help

XYZ Corporation produces a commercial result that is in wide claim by consumers on a gregarious plea. Unfortunately, nigh the fix where it is manufactured there is a great population of dove-tail turtles who are adversely monstrous by contaminants from the fix. XYZ has a filtering regularity that is valuable and any extension in filtering energy reduces their advantage. Dove tailed turtles are not a fortified mark hereafter there are no environmental rules prevalent XYZ’s roll of contaminants.

Clearly, no filtering at all would maximize XYZ’s advantageability. However, a persomal environmental order monitors XYZ’s contaminant roll and maintains a website showing the percentage torpor scold of the dove tailed turtles due to XYZ’s contaminants. XYZ has noticed that the eminent the torpor percentage, the short items are bought and the inferior their advantageability.

Their Marketing Department and Research Order has normal the aftercited Enrichment Function, R(x), as a character of Dove Tail Turtle Torpor developed as decimal between 0 to 1, representing torpor scold:

R(x) = 1 + x – x2; 0 < x ≤ 1

R(x) is developed in billions of dollars and represents the enrichment generated. Since XYZ has unwandering detached costs of one billion dollars, the advantage character, P(x) is fond by P(x) = R(x) – 1.

You accept been compensated as the unversified consultant for XYZ Corporation. They accept asked you to acceleration them optimize their advantage and solicit that you:

1. Find the optimal dove-tail turtle torpor scold percentage that succeed maximize enrichment.

2. State what the ultimatum advantage succeed be.

Discussion:

As a fortunate mathematics student, you abundantly do the math and end up after a while the resolution. Please enclose the answers to questions 1 and 2 in your argument support.

But don’t infer your currency yet. You too comprehend that mathematics is a civilized breath and carries after a while it a actual gregarious province. Are there any holy considerations that you would procure to your client’s study?