Question

The consumer demand curve for Professor Stefan bells is given by

q = (80 − 2p)^2,
where p is the price per bell, and q is the demand in weekly sales. Find the price Professor should charge for his bells to maximize revenue. (Round your answer to the nearest cent.)

Answer 1

To maximize revenue, the professor should charge $40 per bell.

Step-by-step explanation:

To maximize revenue, we need to find the price at which the demand is highest.

We can find this by taking the derivative of the demand function and setting it equal to zero.

Let's find the derivative first:

q = (80 - 2p)2

Take the derivative of both sides with respect to p:

dq/dp = 2(80 - 2p)(-2) = -4(80 - 2p)

Now set dq/dp equal to zero and solve for p:

-4(80 - 2p) = 0

80 - 2p = 0

-2p = -80

p = 40

So the professor should charge $40 per bell to maximize revenue.