Answer :
To calculate the unit variable cost and total fixed cost for maintenance using the high-low method, we need to follow a few steps. Let's go through these in detail.
Step 1: Identify the high and low levels of activity along with their associated costs.
- Low level of activity: 80 direct labor hours with a maintenance cost of [tex]$600. - High level of activity: 200 direct labor hours with a maintenance cost of $[/tex]1,100.
Step 2: Calculate the unit variable cost.
The formula for the unit variable cost is:
[tex]\[ \text{Unit Variable Cost} = \frac{\text{High Cost} - \text{Low Cost}}{\text{High Activity Level} - \text{Low Activity Level}} \][/tex]
Substitute the given values into the formula:
[tex]\[ \text{Unit Variable Cost} = \frac{1100 - 600}{200 - 80} \][/tex]
[tex]\[ \text{Unit Variable Cost} = \frac{500}{120} \][/tex]
[tex]\[ \text{Unit Variable Cost} \approx 4.166666666666667 \][/tex]
Rounded to two decimal places, this is approximately [tex]$4.17. Step 3: Calculate the total fixed cost. Now, use the total cost formula at either the high or low activity level to solve for the total fixed cost. The total cost formula is: \[ \text{Total Cost} = (\text{Unit Variable Cost} \times \text{Activity Level}) + \text{Total Fixed Cost} \] Using the low level of activity (80 direct labor hours): \[ 600 = (4.166666666666667 \times 80) + \text{Total Fixed Cost} \] \[ 600 = 333.33333333333336 + \text{Total Fixed Cost} \] \[ \text{Total Fixed Cost} = 600 - 333.33333333333336 \] \[ \text{Total Fixed Cost} = 266.66666666666663 \] Rounded to two decimal places, this is approximately $[/tex]267.
Summary:
Therefore, using the high-low method, we find:
- The unit variable cost is approximately [tex]$4.17. - The total fixed cost is approximately $[/tex]267.
So the correct answer is:
1) Unit Variable Cost - [tex]$4.17; Total Fixed Cost - $[/tex]267
Step 1: Identify the high and low levels of activity along with their associated costs.
- Low level of activity: 80 direct labor hours with a maintenance cost of [tex]$600. - High level of activity: 200 direct labor hours with a maintenance cost of $[/tex]1,100.
Step 2: Calculate the unit variable cost.
The formula for the unit variable cost is:
[tex]\[ \text{Unit Variable Cost} = \frac{\text{High Cost} - \text{Low Cost}}{\text{High Activity Level} - \text{Low Activity Level}} \][/tex]
Substitute the given values into the formula:
[tex]\[ \text{Unit Variable Cost} = \frac{1100 - 600}{200 - 80} \][/tex]
[tex]\[ \text{Unit Variable Cost} = \frac{500}{120} \][/tex]
[tex]\[ \text{Unit Variable Cost} \approx 4.166666666666667 \][/tex]
Rounded to two decimal places, this is approximately [tex]$4.17. Step 3: Calculate the total fixed cost. Now, use the total cost formula at either the high or low activity level to solve for the total fixed cost. The total cost formula is: \[ \text{Total Cost} = (\text{Unit Variable Cost} \times \text{Activity Level}) + \text{Total Fixed Cost} \] Using the low level of activity (80 direct labor hours): \[ 600 = (4.166666666666667 \times 80) + \text{Total Fixed Cost} \] \[ 600 = 333.33333333333336 + \text{Total Fixed Cost} \] \[ \text{Total Fixed Cost} = 600 - 333.33333333333336 \] \[ \text{Total Fixed Cost} = 266.66666666666663 \] Rounded to two decimal places, this is approximately $[/tex]267.
Summary:
Therefore, using the high-low method, we find:
- The unit variable cost is approximately [tex]$4.17. - The total fixed cost is approximately $[/tex]267.
So the correct answer is:
1) Unit Variable Cost - [tex]$4.17; Total Fixed Cost - $[/tex]267
