Answer:
The function would be:
[tex]C(m)=30+0.50m[/tex]
Because the rent cost $30 initially, and then $0.50 per mile additionally. So, the $30 is a constant, and the $0.50 is variable, so it has to be with the independent variable.
However, we need to set one restriction, because the problem says that the total mileage is limited to 100 miles. This means that [tex]m[/tex] cannot be more than 100 miles, or it could be equal or less than 100 miles.
So, this restriction would be:
[tex]m\leq 100[/tex]
Also, if miles are restricted, then, costs are also restricted to less than 100 miles:
[tex]C(m)=30+0.50(100)=80[/tex]
Therefore, the cost is not higher than $80:
[tex]C\leq 80[/tex]
Therefore, the function and restrictions would be:
[tex]C(m)=30+0.50m[/tex]
[tex]m\leq 100[/tex]
[tex]C\leq 80[/tex]
