Please help me you guys, this is the 3rd time I have posted this question.
Is anybody going to help me with this problem?
A widget factory has fixed costs of 35 billion dollars and variable costs of 781 million dollars per widget. The revenue (in $ billions) from selling x number of widgets is given by the following for x between 0 and 60.
R(x) = 0.11(60x - x^2)
What is the marginal profit (in $ billions per widget) at production level x = 19 widgets? (Give your answer correct to 3 decimal places.)
$ _______ billion per widget
thanks
To find the marginal profit at a given production level x = 19 widgets, we need to calculate the derivative of the revenue function with respect to x, and then substitute x = 19 into the derivative.
1. Let's start by finding the derivative of the revenue function R(x) = 0.11(60x - x^2) with respect to x.
To do this, we can apply the power rule and constant multiple rule of differentiation:
dR(x)/dx = 0.11 * d(60x - x^2)/dx
dR(x)/dx = 0.11 * (60 - 2x)
2. Now, substitute x = 19 into the derivative to find the marginal profit at production level x = 19:
dR(x)/dx = 0.11 * (60 - 2*19)
dR(x)/dx = 0.11 * (60 - 38)
dR(x)/dx = 0.11 * 22
dR(x)/dx = 2.42
So, the marginal profit at production level x = 19 widgets is $2.42 billion per widget.