Question

You have been asked by the Royal University Hospital to assist in estimating their cost structure so that management is better able to plan and control the business affairs of the Magnetic Resonance Imaging (MRI) department. The manager of the MRI department has asked you to assist in classifying the utility costs. Utility cost are very high in the department given that the MRI machine cannot be turned off due to the long warm-up period required for its use. When the MRI machine is used to scan a patient, it consumes an additional burst of power. You have been provided with the following data on utility costs and the use of the MRI scanner for the past year:

Month	# of MRIs	Total Utility Costs
January	455	$501,200
February	482	511,210
March	587	611,000
April	550	622,000
May	415	467,000
June	535	550,000
July	568	601,000
August	498	504,500
September	401	492,000
October	525	582,000
November	500	507,800
December	511	525,000

The hospital would like to be able to estimate their patient costs using the number of patients as the basis for estimation. They have approached you for help.

Required

1. Based on the data provided in Part 1 (above), what would you advise, and/or say to the manger of the MRI department if they asked to approximate the total utility cost if:

1. The number of scans was expected to be 540 in a given month?
2. The number of scans was expected to be 0 (zero) in a given month?
3. The number of scans was expected to be 3,105 in a given month?
4. Prepare a Scatter-graph by plotting the monthly data (number of MRIs and total utility cost). Plot (on the scattergraph) and label each of the axis titles and lines for fixed costs, total costs, and variable costs. Lastly, using the scattergraph, method prepare a cost equation.

Answer 1

Requirement 1: Compute total utility cost when the expected MRI scans are 540 per month as follows

Total utility cost          = Fixed cost + (Variable cost per MRI scan × Number of MRI scans)

                                    = $135,270 + ($804.96 × 540 per MRI scan)

                                    = $569,946

Requirement 2: Compute total utility cost when the expected MRI scans are 0 per month as follows

Total utility cost          = Fixed cost + (Variable cost per MRI scan × Number of MRI scans)

                                    = $135,270 + ($804.96 × 0 per MRI scan)

                                    = $135,270

Requirement 3: Compute total utility cost when the expected MRI scans are 3,105 per month as follows

Total utility cost          = Fixed cost + (Variable cost per MRI scan × Number of MRI scans)

                                    = $135,270 + ($804.96 × 3,105 per MRI scan)

                                    = $2,634,658

Note: Compute fixed and variable costs using the intercept and slope functions of Excel as follows:

Requirement 4: Prepare the scatter-graph as follows

Prepare the total cost equation as follows

Y = $135,270 + $804.96X