Mountain View Hospital in Alberta 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 to secure data 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 strictly fixed cost behaviour. Utilities costs are very high in the department due to a CT scanner that draws a large amount of power and is kept running at all times. The scanner cannot be turned off due to the long warm-up period required for its use. When the scanner is used to scan a patient, it consumes an additional burst of power. The assistant has accumulated the following data on utilities costs and use of the scanner since the first of the year:

The chief administrator has informed her assistant that the utilities cost is probably a mixed cost that will have to be broken down into its variable and fixed cost elements by use of a scattergraph. The assistant feels, however, that if an analysis of this type is necessary, the high?low method should be used because it is easier and quicker to use than other methods. The controller has suggested that there might 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 scattergraph 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 regression line to the plotted points by visual inspection, and estimate a cost formula for utilities.

3. Estimate a cost formula using least-squares regression (use a spreadsheet).

4. Comment on the differences among the three cost formulas estimated above. Which one would you use?

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Number of Utilities Month Scans Cost $ 4,250 January 40 6,300 February 85 March 100 7,000 150 April 10,400 May 200 14,000 June 110 8,500 July 260 16,000 August 160 11,700 September 210 15,100 October 180 13,500