Problem:
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:
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Direct
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Tons Mined
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Labor_Hours
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Utilities
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Quarter
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(000)
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(000)
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Cost
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Year 1
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First
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.............
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15
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5
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$ 50,000.00
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|
Second
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.............
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11
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3
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$ 45,000.00
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|
Third
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.............
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21
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4
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$ 60,000.00
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Fourth
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.............
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12
|
6
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$ 75,000.00
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Year 2
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|
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|
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First
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.............
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18
|
10
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$100,000.00
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Second
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.............
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25
|
9
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$105,000.00
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|
Third
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.............
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30
|
8
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$ 85,000.00
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|
Fourth
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.............
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28
|
11
|
$120,000.00
|
Required to answer:
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?
Check Figure
(1) Y=$28,352+$2,582X