Can someone explain this in word form Their Marketing Depart

Can someone explain this in word form? 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. This is what I came up with: R(x) = 1 + x – x2 Finding the optimal dove tail mortality rate R(x) = d/dx (1 + x – x2) = 1 – 2x R(x) = 0 x = 0.5 The optimal dove tail mortality rate is 50% or 0.5 R(x) = 1 + 0.5 – (0.5)2 = 1 + 0.5 – 0.25 = 1.25 Maximum profit will be P(x) = R(x) – 1 = 1.25 – 1 = 0.25 billion dollars

Solution

R(x) = 1 + x – x2; 0 < x 1 R(x) is expressed in billions of dollars and represents the revenue generated.

we have to find mortality for maximum revenue

maximum revenue :dR/dx =0    and solve for x ; x = 0.5

Corresponding to this x = 0.5 we get maximum revenue.

Now for profit we know P(x) = R(x) -1 = 1 +x - x^2 - 1 = x - x^2

find dP/dx = 1 -2x ; x = 0.5 .So, x remains same

find maximu profit for x =0.5 which you got as P(0.5) = 0.25 billion dollars