Respuesta :
the maximum annual variable he can have is $2140
Explanation:Total miles that Leann will drive during the year = 14000 miles
Annual fixed cost = $2200
Goal for cost per mile: $0.31 or less
This means the goal can be $0.31 but cannot exceed this
mathematically: ≤ $0.31
To find the maximum annual variable cost:
Total annual cost = annual variable cost + annual fixed cost
Total annual cost = annual variable cost + 2200
Calculating cost per mile:
[tex]\begin{gathered} \frac{total\text{ annual cost}}{nu\text{mber of miles covered}}=\text{ }\cos t\text{ per mile} \\ \\ In\text{ this case our cost per mile cannot exc}eed\text{ \$0.31, so the formula becomes:} \\ \frac{total\text{ annual cost}}{nu\text{mber of miles covered}}\text{ }\le\text{ }0.31 \end{gathered}[/tex][tex]\begin{gathered} \frac{\text{annual variable cost + 2200}}{14000}\text{ }\le\text{ 0.31} \\ \\ \text{cross multiply:} \\ \text{annual variable cost }+\text{ 2200 }\le\text{ 0.31(14000)} \\ \text{annual variable cost + 2200 }\le\text{ 4340} \end{gathered}[/tex][tex]\begin{gathered} \text{subtract 2200 from both sides:} \\ \text{annual variable cost + 2200 - 2200 }\le\text{ 4340 - 2200} \\ \text{annual variable cost }\le2140 \end{gathered}[/tex]From our result above ≤ 2140 means our annual variable cost can be 2140, less than this number but cannot exceed this number.
Hence, the maximum annual variable he can have is $2140