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

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

where is the amount of money and is the number of hours.

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

9 x 8 divided by (5-3)=36