Bethany Link delivers parts for several local auto parts stores. She charges clients $0.75 per mile driven. She has determined that if she drives 2,100 miles in a month, her average operating cost is $0.55 per mile. If Bethany drives 4,200 miles in a month, her average operating cost is $0.40 per mile.


Required:
a. Using the high-low method, determine Bethany’s variable and fixed operating cost components. (Round your cost per unit answer to 2 decimal place.)
1. variable cost per unit= ?
2. fixed cost= ?


b. Complete the contribution margin income statement for the business last month, when Bethany drove 2,400 miles. (Assume this falls within the relevant range of operations).

a. The high-low method involves using the highest and lowest activity levels and their corresponding costs to determine the variable and fixed cost components.

Let's start with the high and low activity levels and their corresponding costs:

High level (4,200 miles):
Operating cost = $0.40 per mile
Total cost for 4,200 miles = $0.40/mile * 4,200 miles = $1,680

Low level (2,100 miles):
Operating cost = $0.55 per mile
Total cost for 2,100 miles = $0.55/mile * 2,100 miles = $1,155

To find the variable cost per unit, we subtract the fixed cost from the total cost at either the high or low level:

Variable cost per unit = (Total cost at high level - Fixed cost) / Number of units at high level
Variable cost per unit = ($1,680 - Fixed cost) / 4,200 miles

Variable cost per unit = ($1,155 - Fixed cost) / 2,100 miles

Setting the two equations equal to each other:
($1,680 - Fixed cost) / 4,200 miles = ($1,155 - Fixed cost) / 2,100 miles

Cross-multiplying:
2,100 * ($1,680 - Fixed cost) = 4,200 * ($1,155 - Fixed cost)

Simplifying the equation:
3,528,000 - 2,100 * Fixed cost = 4,842,000 - 4,200 * Fixed cost

Rearranging the equation:
-2,100 * Fixed cost + 4,200 * Fixed cost = 4,842,000 - 3,528,000

1,200 * Fixed cost = 1,314,000

Fixed cost = 1,314,000 / 1,200

Fixed cost = $1,095

Now that we have the fixed cost, we can substitute it back into one of the equations to find the variable cost per unit:

Variable cost per unit = ($1,680 - Fixed cost) / 4,200 miles

Variable cost per unit = ($1,680 - $1,095) / 4,200 miles

Variable cost per unit = $585 / 4,200 miles

Variable cost per unit ≈ $0.14

Therefore, the answers are:
1. Variable cost per unit = $0.14
2. Fixed cost = $1,095

b. To complete the contribution margin income statement for the business last month when Bethany drove 2,400 miles, we would need additional information such as revenue, other expenses, and the number of units sold.