A workout 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

Question

How many paying customers are needed to made a profit? thank you I think it is 19 but I am not sure

Answer 1

Profit will be positive when

 

0.4x²-7.2x≥0;

 

The minimum number of customers is determined by considering the case, when 0.4x²-7.2x=0

 

This expression is equivalent to:

 

0.4x-7.2=0 (x>0, number of customers can not be zero, therefore we can divide both side by x)

 

From this we obtain:

 

x=7.2/0.4=18

 

So 18 customers give zero profit, therefore any number greater than 18 will suffice.