To find the variable cost per machine hour using the high-low method, follow these steps:
### Step 1: Identify the high and low points
1. High Point: Determine the highest and lowest machine hours from the data.
- The highest machine hours is 2,900 hours (in March).
- The lowest machine hours is 2,100 hours (in January).
2. Corresponding Costs: Identify the costs that correspond to these high and low points.
- The cost for the high point (2,900 hours) is \[tex]$6,400 (March).
- The cost for the low point (2,100 hours) is \$[/tex]4,800 (January).
### Step 2: Compute the Change in Cost and Change in Machine Hours
1. Change in Cost:
[tex]\[
\Delta \text{Cost} = \$6,400 - \$4,800 = \$1,600
\][/tex]
2. Change in Machine Hours:
[tex]\[
\Delta \text{Machine Hours} = 2,900 \text{ hours} - 2,100 \text{ hours} = 800 \text{ hours}
\][/tex]
### Step 3: Calculate the Variable Cost per Machine Hour
Using the high-low method, the variable cost per machine hour is calculated by dividing the change in cost by the change in machine hours:
[tex]\[
\text{Variable Cost per Machine Hour} = \frac{\Delta \text{Cost}}{\Delta \text{Machine Hours}} = \frac{\$1,600}{800 \text{ hours}} = \$2.00 \text{ per hour}
\][/tex]
### Step 4: Select the Correct Option
Among the given options, the correct variable cost per machine hour is:
[tex]\[
\boxed{\$2.00}
\][/tex]
So, the variable cost per machine hour by using the high-low method is \$2.00 per hour.
