Question: Lorenzo operates a brushless car wash. Incoming cars are put on an automatic, continuously moving conveyor belt. A car is washed as the conveyor belt carries it from the start station to the finish station. After the car moves off the conveyor belt, workers dry it and clean and vacuum the inside. Workers are managed by a single supervisor.
Lorenzo's accountant wants to estimate total costs in December, when 10,400 cars are expected to be washed. She uses two different methods to estimate total December costs, account analysis and high-low, with number of cars washed as the independent variable for both methods.
For the account analysis method, she developed cost function parameter estimates by analyzing actual costs in June, when 11,900 cars were washed. The following are June total costs and her fixed cost estimates:
| Cost Item |
Total Cost
|
Fixed Portion
|
| Soap, cloths, and supplies |
$7,140
|
$0
|
| Water |
$4,760
|
$0
|
| Car wash labor |
$34,810
|
$2,680
|
| Power for conveyor |
$12,220
|
$2,700
|
| Supervisor and cashier |
$3,300
|
$3,300
|
For the high-low method, she developed cost function parameter estimates by using the actual costs in April and May, when 8,400 and 11,500 cars were washed, respectively. The following are total costs for these two months:
| Cost Item |
April
|
May
|
| Soap, cloths, and supplies |
$4,200
|
$5,750
|
| Water |
$5,040
|
$6,900
|
| Car wash labor |
$26,520
|
$35,200
|
| Power for conveyor |
$11,740
|
$15,150
|
| Supervisor and cashier |
$4,650
|
$4,650
|
| Total |
$52,150
|
$67,650
|
Required [round per-unit costs to the nearest cent and total costs to the nearest dollar.]
Using the high-low method, what is the accountant's estimate of total fixed costs for December?