Can someone explain this in word form? Their Marketing Department and Research G
ID: 3035836 • Letter: C
Question
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
Explanation / Answer
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