To determine the variable cost per unit and the total fixed costs using the high-low method, follow these steps:
### Step 1: Identify high and low activity levels
From the given data:
- April: Total Cost = \[tex]$111,600, Production = 284,000 units
- May: Total Cost = \$[/tex]89,000, Production = 162,200 units
- June: Total Cost = \[tex]$100,400, Production = 235,200 units
The high point (highest production) is April with 284,000 units. The low point (lowest production) is May with 162,200 units.
### Step 2: Calculate the variable cost per unit
Calculate the change in cost and the change in production between the high and low points.
- Change in cost = Cost_high - Cost_low = \$[/tex]111,600 - \[tex]$89,000 = \$[/tex]22,600
- Change in production = Production_high - Production_low = 284,000 units - 162,200 units = 121,800 units
Variable cost per unit is:
[tex]\[ \text{Variable Cost per Unit} = \frac{\text{Change in Cost}}{\text{Change in Production}} = \frac{22,600}{121,800} = 0.19 \][/tex]
### Step 3: Calculate the total fixed costs
Using the high point (April) for calculation:
[tex]\[ \text{Total Fixed Costs} = \text{Total Cost} - (\text{Variable Cost per Unit} \times \text{Production}) \][/tex]
[tex]\[ \text{Total Fixed Costs} = \$111,600 - (0.19 \times 284,000) = \$111,600 - \$53,960 = \$57,640 \][/tex]
### Conclusion
The variable cost per unit is \[tex]$0.19 and the total fixed costs are \$[/tex]57,640.
Thus, the correct answer is:
d. \[tex]$0.19 per unit and \$[/tex]57,640, respectively.
