Alright, let's solve this step-by-step using the high-low method.
### Step 1: Identify the highest and lowest levels of activity
From the given data:
- The highest level of production is 4,800 bottles in March with a total cost of [tex]$198,000.
- The lowest level of production is 3,300 bottles in May with a total cost of $[/tex]148,500.
### Step 2: Calculate the variable cost per bottle
The variable cost per bottle can be determined by the change in total cost divided by the change in the number of bottles produced.
[tex]\[
\text{Variable Cost per Bottle} = \frac{\text{Change in Cost}}{\text{Change in Production}}
\][/tex]
Substitute the values:
[tex]\[
\text{Variable Cost per Bottle} = \frac{\$198,000 - \$148,500}{4,800 - 3,300}
\][/tex]
[tex]\[
\text{Variable Cost per Bottle} = \frac{\$49,500}{1,500} = \$33.00 \text{ per bottle}
\][/tex]
### Step 3: Calculate the fixed cost
We use the total cost at either the high or low level to calculate the fixed cost. Let's use the cost at the highest production level (4,800 bottles).
[tex]\[
\text{Total Cost} = \text{Fixed Cost} + (\text{Variable Cost per Bottle} \times \text{Number of Bottles})
\][/tex]
Rearrange to solve for the fixed cost:
[tex]\[
\text{Fixed Cost} = \text{Total Cost} - (\text{Variable Cost per Bottle} \times \text{Number of Bottles})
\][/tex]
Substitute the values:
[tex]\[
\text{Fixed Cost} = \$198,000 - (\$33.00 \times 4,800)
\][/tex]
[tex]\[
\text{Fixed Cost} = \$198,000 - \$158,400 = \$39,600
\][/tex]
### Step 4: Calculate the total cost for the planned production
Given that the planned production is 13,200 bottles:
[tex]\[
\text{Total Cost} = \text{Fixed Cost} + (\text{Variable Cost per Bottle} \times \text{Planned Production})
\][/tex]
Substitute the values:
[tex]\[
\text{Total Cost} = \$39,600 + (\$33.00 \times 13,200)
\][/tex]
[tex]\[
\text{Total Cost} = \$39,600 + \$435,600 = \$475,200
\][/tex]
### Conclusion
The total cost for producing 13,200 bottles using the high-low method will be \[tex]$475,200.
Therefore, the correct option is:
2) \$[/tex]475,200
