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Their Marketing Department and Research Group has established the following Revenue Function R(x) as a function

Question

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.

Math