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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

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