this is a economic task Alg 1b

Question

a work gym's annual profit is modeled by the equation p=0.4x^2-7.2x, where x is the number of paying customers. How many paying customers are needed to make a profit?

Answer 1

P = 0.4x² - 7.2x

 

To make a profit, we need P > 0

 

0.4x² - 7.2x > 0

 

0.4x² > 7.2x          [Added 7.2x to both sides]

 

0.4x > 7.2              [Divided both sides by x]

 

Solve for x

Answer 2

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

Since it’s given you the underlying profit equation you just want to solve for the places where p(x) > 0. To do that I would start by setting the p(x) equation equal to 0 to find the number of customers where the profit is exactly zero.

0.4x^2 – 7.2x = 0

x(0.4x – 7.2) = 0

x = 0 or

0.4x = 7.2

x = 7.2 / 0.4 = 18

so in between x = 0 and x = 18, the gym is making a loss, meaning that p(x) is positive for values of x greater than 18

the number of paying customers must be greater than 18 in order for the gym to make a profit

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 :)