Question

The total cost of hiring paul the plumber is a function of the required number of hours needed to complete the repair. Paul charges $40 per hour up to maximum of 8 hours, plus a $75 service charge what is the greatest value in the range for this situation

Answer 1

Paul surely charges 75 dollars, and then he adds 40 dollars per hours. This means that the expression for the money he asks is

$m = 75+40h$

where $m$ is the amount of money and $h$ is the number of hours.

Since $h$ can be at most 8, this is the case that generates the highest money, so if we plug $h=8$ we have

$m = 75+40\cdot 8 = 75 + 320 = 395$