XYZ Corporation produces a commercial product that is in great demand by consumers on a national basis.
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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.
Corporation
A Corporation is a legal form of business that is separate from its owner. In other words, a corporation is a business or organization formed by a group of people, and its right and liabilities separate from those of the individuals involved. It may...
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Related Book For
Management Accounting
ISBN: 9780730369387
4th Edition
Authors: Leslie G. Eldenburg, Albie Brooks, Judy Oliver, Gillian Vesty, Rodney Dormer, Vijaya Murthy, Nick Pawsey
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