Spider Industries is a U.S.-based company that test-marketed an electronic cobweb destroyer in Japan. The company's revenue, R, is a function of the number of destroyers sold, x, using the following formula R = 160x -0.2x^2.
If the company sold their destroyers for $180 each, what is the maximum revenue Spider Industries could bring in?
I thought it was $32,000 but that was incorrect.
Well, the equation is a parabola.The roots are x=0 and x=800 check that.
So the maximum must be at x=400
R=x(160-.2x)=400*(160-.2*400)=160*80
= you do it.
To find the maximum revenue Spider Industries could bring in, we need to determine the value of x that maximizes the revenue equation R = 160x - 0.2x^2.
To find this value, we can use a technique called calculus. We need to find the derivative of the revenue function, set it equal to zero, and solve for x.
The derivative of the revenue function R with respect to x is given by dR/dx = 160 - 0.4x.
Setting this derivative equal to zero, we have:
160 - 0.4x = 0
Solving for x, we get:
0.4x = 160
x = 160/0.4
x = 400
Therefore, at x = 400, the revenue function has a maximum.
Now we can substitute this value of x back into the revenue function to find the maximum revenue:
R = 160x - 0.2x^2
R = 160(400) - 0.2(400^2)
R = 64,000 - 0.2(160,000)
R = 64,000 - 32,000
R = $32,000
Apologies, but it seems that your initial answer of $32,000 was correct. The maximum revenue that Spider Industries could bring in is indeed $32,000.