Final answer:
Using the high-low method, the fixed cost of electricity per month at the Cheyenne Hotel in Big Sky, Montana is estimated to be $1,396.64, and the variable cost of electricity per occupancy-day is estimated to be $1.56.
Step-by-step explanation:
To estimate the fixed cost of electricity per month and the variable cost of electricity per occupancy-day using the high-low method, we need to identify the high and low points. The high month had 2,406 occupancy days and $5,148 in electrical costs, while the low month had 124 occupancy days and $1,588 in electrical costs.
To find the variable cost per occupancy-day, we can calculate the difference in electrical costs between the high and low months and divide it by the difference in occupancy days. In this case, the difference in electrical costs is $5,148 - $1,588 = $3,560, and the difference in occupancy days is 2,406 - 124 = 2,282.
Dividing the difference in electrical costs by the difference in occupancy days gives us the variable cost per occupancy-day: $3,560 / 2,282 = $1.56 per occupancy-day.
To find the fixed cost of electricity per month, we can take the total electrical costs of either the high or low month and subtract the variable cost (calculated above) multiplied by the respective number of occupancy days. Let's use the high month for this calculation. The total electrical costs for the high month is $5,148, and the number of occupancy days is 2,406.
Using the formula: Fixed Cost = Total Cost - (Variable Cost per Occupancy-day * Number of Occupancy Days), we have: Fixed Cost = $5,148 - ($1.56 * 2,406) = $5,148 - $3,751.36 = $1,396.64 per month.