To determine the average total cost of producing the third unit of output, we need to follow these steps:
1. Identify the Total Fixed Cost for each unit produced:
- For the first unit, the Total Fixed Cost is [tex]\( \$120 \)[/tex].
- The Total Fixed Cost for the first three units is the same, i.e., [tex]\( \$120 \)[/tex] as it typically remains constant for the first three units, based on the provided data.
2. Identify the Total Variable Costs for each unit produced:
- For the first unit, the Total Variable Cost is [tex]\( \$30 \)[/tex].
- For the second unit, the Total Variable Cost is [tex]\( \$40 \)[/tex].
- For the third unit, the Total Variable Cost is [tex]\( \$60 \)[/tex].
3. Calculate the Total Cost for each unit produced:
- Total Cost for the first unit is the sum of the Total Fixed Cost and the Total Variable Cost for the first unit:
[tex]\[
120 + 30 = 150 \text{ dollars}
\][/tex]
- Total Cost for the second unit is the sum of the Total Fixed Cost and the Total Variable Cost for the second unit:
[tex]\[
120 + 40 = 160 \text{ dollars}
\][/tex]
- Total Cost for the third unit is the sum of the Total Fixed Cost and the Total Variable Cost for the third unit:
[tex]\[
120 + 60 = 180 \text{ dollars}
\][/tex]
4. Calculate the Total Cost of producing all three units:
[tex]\[
150 + 160 + 180 = 490 \text{ dollars}
\][/tex]
5. Determine the Average Total Cost for producing the third unit:
The Average Total Cost for producing the third unit is the Total Cost of producing three units divided by the number of units:
[tex]\[
\frac{180}{3} = 60 \text{ dollars}
\][/tex]
Therefore, the average total cost of producing the third unit of output is [tex]\(\$60\)[/tex].
