Management planning and decision making

Check Figure
(1) Y=$28,352+$2,582X

The Hard Rock Mining Company is developing cost formulas for management planning and decision making purposes. The company's cost analyst has concluded that utilities cost is a mixed cost, and he is attempting to find a base with which the cost might be closely correlated. The controller has suggested that tons mined might be a good base to use in developing a cost formula. The production superintendent disagrees; she thinks that direct labor hours would be a better base. The cost analyst has decided to try both bases and has assembled the following information:

Direct
Tons Mined Labor_Hours Utilities
Quarter (000) (000) Cost

Year 1
First ............. 15 5 $ 50,000.00
Second ............. 11 3 $ 45,000.00
Third ............. 21 4 $ 60,000.00
Fourth ............. 12 6 $ 75,000.00
Year 2
First ............. 18 10 $100,000.00
Second ............. 25 9 $105,000.00
Third ............. 30 8 $ 85,000.00
Fourth ............. 28 11 $120,000.00

Required:
1. Using tons mined as the independent (X) variable:
a. Determine a cost formula for utilities cost using the least-squares regression method. (The variable cost you compute will be in thousands of tons. It can be left in this form, or you can convert your variable cost to a per ton basis by dividing it by 1,000)

B. Prepare a scatter graph and plot the tons mined and utilities cost. (Place cost on the vertical axis and tons mined on the horizontal axis.) Fit a straight line to the plotted points using the cost formula determined in (a) above.

2. Using direct labor-hours as the independent (x) variable, repeat the computations in (a) and (b) above.

3. Would you recommend that the company uses tons mined or direct labor- hours as a base for planning utilities cost?