With the data of the statement we can write the following cost functions for each company:
A) Charge of company A
[tex]C_A(m)=114[/tex]B) Charge of company B
[tex]C_B(m)=75+0.60\cdot m[/tex]We want to know for what mileages will Company A charge less than Company B.
We can write the last sentence as:
[tex]C_A(m)\leq C_B(m)[/tex]Replacing with the functions of above:
[tex]\begin{gathered} C_A(m)\leq C_B(m) \\ 114\leq75+0.60\cdot m \\ 114-75\leq0.60\cdot m \\ 39\leq0.60\cdot m \\ \frac{39}{0.60}\leq m \\ 65\leq m \end{gathered}[/tex]We see that if want the first inequality to be satisfied, the number of miles must be greater than 65 miles.
