Question

A plumber charges $40 per hour for labor with a minimum labor charge of $30. For example, if she
does her repairs in only 0.2 hours, then $40*0.2=$8, which is less than the minimum, so she would
charge $30 for labor. We will assume she can repair any problem in one day – a maximum of 8
hours work. In addition, she charges $1.50 per mile for every mile over 15 miles that she has to
travel to the work site. To answer the following questions, assume you live 27 miles away from the
plumber. (She also charges for parts, but we won’t consider that for now.)
a. Find a piecewise defined function to describe the possible charges for the plumber to repair a
leaky faucet at your home. (There will only be one input variable.)
b. What is the domain of this function?
c. What is the range of this function?
d. What is the total charge if she takes 2.5 hours to complete the repairs?

Answer 1

a. Y = Cost.
X = # of hrs.

Y = 40x + 1.5(27-15),
Y = 40x + 18.

b. Domain = All real values of X.

c. Range = All real values of Y.

d. Y = 40*2.5 + 18 = $118.=Tot. charges