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.
How many destroyers must the company sell to maximize its revenue?
75, 400, or 40.
At maximum revenue, dR/dx = 0
That means 160 - 0.4x = 0
Solve for x.
To find the number of destroyers that will maximize revenue, we need to calculate the derivative of the revenue function and find where it equals zero.
First, let's find the derivative of the revenue function.
R = 160x - 0.2x^2
dR/dx = 160 - 0.4x
Next, set the derivative equal to zero and solve for x.
0 = 160 - 0.4x
0.4x = 160
x = 400
Therefore, the company must sell 400 destroyers to maximize its revenue.
The correct answer is 400.