Question

Leann Wolfe estimates that she will drive 14,000 miles during the year and will have $2,200.00 in annual fixed costs. If her goal is to have a cost per mile of $0.31 or less for her compact car, what is the maximum annual variable cost she can have?

Answer 1

the maximum annual variable he can have is $2140

Step-by-step 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:

`\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}`
`\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}`
`\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}`

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