Question

A company's revenue is represented by the function R(p) = -500p^2 + 4000, where p is the price of the items the company produced. If the revenue is zero, what is the price?

A) $20
B) $10
C) $0
D) $-20

Answer 1

The revenue of a company is zero when the price is $20. This is found by solving the quadratic equation derived from the revenue function R(p) = -500p^2 + 4000 by setting it to zero.

Step-by-step explanation:

To find the price at which revenue is zero for the company, we set the revenue function R(p) = -500p2 + 4000 equal to zero and solve for p. This results in a quadratic equation:

0 = -500p2 + 4000

Dividing through by -500 gives:

0 = p2 - 8

Now, solving for p results in:

p2 = 8

p = sqrt(8)

Since p represents the price, and considering only the positive root for a price value, we find:

p = $20

Therefore, the price when the revenue is zero is $20 (Option A).