18.07.2022 - 02:07

# The Cheyenne Hotel in Big Sky, Montana, has accumulated records of the total electrical costs of the hotel and the number of occupancy-days over the last year. An occupancy-day represents a room rented out for one day. Business is highly seasonal, with pe

Question:

The Cheyenne Hotel in Big Sky, Montana, has accumulated records of the total electrical costs of the hotel and the number of occupancy-days over the last year. An occupancy-day represents a room rented out for one day. Business is highly seasonal, with peaks occurring during the ski season and in the summer.

Month Occupancy-Days Electrical Costs
January 1,736 $4,127 February 1,904$4,207
March 2,356 $5,083 April 960$2,857
May 360 $1,871 June 744$2,696
July 2,108 $4,670 August 2,406$5,148
September 840 $2,691 October 124$1,588
November 720 $2,454 December 1,364$3,529

1. Using the high-low method, estimate the fixed cost of electricity per month and the variable cost of electricity per occupancy-day. Round off the fixed cost to the nearest whole dollar and the variable cost to the nearest whole cent.

2. What other factors other than occupancy-days are likely to affect the variation in electrical costs from month to month.

1. The high-low method estimates the fixed and variable costs using the highest and lowest values of the data set. Firstly, we calculate the variable cost per occupancy-day by choosing the highest and lowest occupancy-days and corresponding electrical costs: Variable cost per occupancy-day = (Electrical cost at highest occupancy-day - Electrical cost at lowest occupancy-day) / (Number of occupancy-days at highest - Number of occupancy-days at lowest) = ($5,148 -$1,871) / (2,406 - 360) = $0.0028 (rounded to the nearest cent) Then, we can use either the highest or lowest data point to calculate the fixed cost as: Fixed cost = Total electrical costs - (Variable cost per occupancy-day x Total occupancy-days) = ($5,148 x 2,406) - ($0.0028 x 20,236) =$2,127 (rounded to the nearest dollar) Therefore, the estimated fixed cost of electricity per month is $2,127, and the estimated variable cost of electricity per occupancy-day is$0.0028. 2. Other factors that may affect the variation in electrical costs from month to month include the weather conditions, maintenance and repair activities, occupancy rates (not just the number of occupancy-days), the usage of appliances and equipment (e.g. heating and cooling systems), and any changes in the electricity rates by the utility company. These factors can vary significantly depending on the season and may cause fluctuations in the electrical consumption and costs.