The high-low method is a simple technique to estimate the variable and fixed portions of costs, particularly useful when costs fluctuate with an underlying factor (in this case, temperature). This method uses the highest and lowest data points in the dataset to create an estimate of the cost relationship.

Step-by-Step Solution:

1. Identify the highest and lowest data points:

   • The lowest average temperature is 10°F in December with a utility cost of $940.
   • The highest average temperature is 60°F in August with a utility cost of $230.

2. Calculate the variable cost per degree (slope):

   The formula to find the variable cost per unit (temperature in this case) is:

   $\text{Variable cost per degree} = \frac{\text{Cost at lowest temp} - \text{Cost at highest temp}}{\text{Lowest temp} - \text{Highest temp}}$

   Substituting the given values:

   $\text{Variable cost per degree} = \frac{940 - 230}{10 - 60} = \frac{710}{-50} = -14.2 \, \text{(dollars per degree)}$

   This indicates that for every 1°F increase in temperature, the utility cost decreases by $14.20.

3. Calculate the fixed cost:

   Now, using either the highest or lowest data point, we can determine the fixed cost. Using the low point (December, 10°F, $940):

   $\text{Fixed cost} = \text{Cost at 10°F} - (\text{Variable cost per degree} \times 10°F)$

   $\text{Fixed cost} = 940 - (-14.2 \times 10) = 940 + 142 = 1082$

   So, the fixed cost (the cost that does not vary with temperature) is $1082.

4. Estimate utility cost for January (5°F) and February (40°F):

   Using the cost equation:

   $\text{Utility Cost} = \text{Fixed cost} + (\text{Variable cost per degree} \times \text{Temperature})$

   • For January (forecasted temperature: 5°F):

     $\text{Utility Cost} = 1082 + (-14.2 \times 5) = 1082 - 71 = 1011$

     So, the estimated utility cost for January is $1011.

   • For February (forecasted temperature: 40°F):

     $\text{Utility Cost} = 1082 + (-14.2 \times 40) = 1082 - 568 = 514$

     So, the estimated utility cost for February is $514.

Summary:

• Estimated utility cost for January (5°F): $1011.
• Estimated utility cost for February (40°F): $514.

Would you like any additional details on this calculation?

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Here are 5 related questions for further exploration:

1. How does the high-low method compare to regression analysis in terms of accuracy?
2. What factors besides temperature might impact utility costs in this scenario?
3. How would adding data for an unusually warm month affect the high-low method estimates?
4. Can the high-low method be used to predict electricity usage alone? Why or why not?
5. What other methods could Horizon BP use to forecast utility costs?

Tip: The high-low method is best used when the cost relationship is linear and there are no outliers affecting the extremes.