Problem:
Pleasant View Hospital of British Columbia has just hired a new chief administrator who is anxious to employ sound management and planning techniques in the business affairs of the hospital. Accordingly, she has directed her assistant to summarize the cost structure existing in the various departments so that data will be available for planning purposes.
The assistant is unsure how to classify the utilities costs in the Radiology Department since these costs do not exhibit either strictly variable or fixed cost behavior. Utilities costs are very high in the department due to a CAT scanner that draws a large amount of power and that is kept running at all times. The scanner can't be turned off due to the long warm-up period required for its use. When the CAT scanner is used to scan a patient, it consumes an additional burst of power. The assistant has accumulated the following data on the utilities costs and use of the CAT scanner since the first of the year.
Month Number of Scans Utilities Cost
January 60 $2,640
February 70 3,120
March 90 3,480
April 120 3,960
May 100 3,600
June 130 4,320
July 150 4,800
August 140 4,320
September 110 3,720
October 80 3,000
The chief administrator has informed her assistant that the cost is probably a mixed cost that will have to be broken down into its variable and fixed cost elements using a scatter graph. The assistant feels, however, that if an analysis of this type is necessary, then the high-low method should be used, since it is easier and quicker. The controller has suggested that there may be a better approach.
Required:
1. Using the high-low method, estimate a cost formula for utilities. Express the formula in the form Y = a + bX. (The variable rate should be stated in terms of cost per scan.)
2. Prepare a scatter graph by plotting the above data on a graph. (The number of scans should be placed on the horizontal axis, and utilities cost should be placed on the vertical axis.) Fit a straight line to the plotted points by visual inspection and estimate a cost formula for utilities.