R(x) = 400x − 0.5x2, where x is the number of apartments booked. What number of apartments booked produces the maximum revenue?

Question

College Algebra word problem. No idea what I'm doing

Answer 1

Hello, thank you for taking the time to post your question!

Since this one is a parabola that opens downward, the vertex is going to represent the maximum value. So we can take

x = -b/2a = -400 / 2(-0.5) = -400 / -1 = 400

meaning that 400 apartments booked produces the maximum revenue

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Hi Maya

For a quantity to be Maximum its first derivative should be equal to zero

 

dR/dx = 400 - 0.5* 2 *X = 0

 

Which means X= 400 =Number of apartments

 

and the Max revenue =  400* 400 - 0.5 * 400*400 =160000 - 80000 = 80000

 

For any other value of X the revenue will be less than 80000

Try that for 350 or 450