<u>Solution and Explanation:</u>
<u>Step 1
</u>
Consider the given information:
Reimbursement = 36 cents per mile
Fixed cost per year = $2,052 minus 205200 cents
Direct variable cost = 14.4 cents per mile
<u>Step 2
</u>
At the break-even point, total cost becomes equal to the total revenue.
Suppose it takes Q miles for ARto reach break-even.
Step1: Calculate the total cost of AR when the car cover Q miles, as shown below:
Total Cost = Fixed cost + Variable Cost
= 205,200 + 14.4 Q
<u>Step 2</u> Calculate the total revenue (reimbursement) of AR when the car covers Q miles, as shown below:
Total Revenue = Reimbursement multiply with Total miles
= 36Q
<u>Step 3:</u> Calculate the break-even miles for the car, as shown below:
At break-even, Total cost = Total revenue
205,200 plus 14.4Q = 36Q
36Q minus 14.4Q = 205,200
21.6Q = 205,200
Q = 205,200 divide by 21.6
Q = 9,500 miles
Hence, AR should drive 9,500 miles to break-even.