Questions: Your cousin Vinnie owns a painting company with fixed costs of 150 and the following schedule for variable costs: Quantity (Houses Painted per Month) Variable Cost (Dollars) Average Fixed Cost (Dollars) Average Variable Cost (Dollars) Average Total Cost (Dollars) --------------- 1 15 ∇ ∇ v 2 35 ∇ ∇ 3 60 ∇ ∇ v 4 90 ∇ v ∇ 5 135 V ✓ ∇ 6 240 ∇ V ∇ 7 480 ✓

Your cousin Vinnie owns a painting company with fixed costs of 150 and the following schedule for variable costs:

Quantity (Houses Painted per Month) Variable Cost (Dollars) Average Fixed Cost (Dollars) Average Variable Cost (Dollars) Average Total Cost (Dollars)
---------------
1 15 ∇ ∇ v
2 35 ∇ ∇
3 60 ∇ ∇ v
4 90 ∇ v ∇
5 135 V ✓ ∇
6 240 ∇ V ∇
7 480 ✓

Transcript text: Your cousin Vinnie owns a painting company with fixed costs of $\$ 150$ and the following schedule for variable costs: \begin{tabular}{|c|c|c|c|c|} \hline \begin{tabular}{l} Quantity \\ (Houses Painted per Month) \end{tabular} & \begin{tabular}{l} Variable Cost \\ (Dollars) \end{tabular} & \begin{tabular}{l} Average Fixed Cost \\ (Dollars) \end{tabular} & \begin{tabular}{l} Average Variable Cost \\ (Dollars) \end{tabular} & Average Total Cost (Dollars) \\ \hline 1 & 15 & $\nabla$ & $\nabla$ & $v$ \\ \hline 2 & 35 & $\nabla$ & & $\nabla$ \\ \hline 3 & 60 & $\nabla$ & $\nabla$ & v \\ \hline 4 & 90 & $\nabla$ & $v$ & $\nabla$ \\ \hline 5 & 135 & V & $\checkmark$ & $\nabla$ \\ \hline 6 & 240 & $\nabla$ & V & $\nabla$ \\ \hline 7 & 480 & \ & $\checkmark$ & \\ \hline \end{tabular}

Solution

Solution Steps

To solve this problem, we need to calculate the missing values in the table using the given fixed costs and variable costs. The key formulas to use are:

Average Fixed Cost (AFC) = Fixed Costs / Quantity
Average Variable Cost (AVC) = Variable Costs / Quantity
Average Total Cost (ATC) = (Fixed Costs + Variable Costs) / Quantity

We'll iterate over the quantities and use these formulas to fill in the missing values.

Step 1: Calculate Average Fixed Cost (AFC)

The Average Fixed Cost (AFC) is calculated using the formula: $AFC = \frac{Fixed \, Costs}{Quantity}$ For each quantity, we find:

For $Q = 1$ : $AFC = \frac{150}{1} = 150.00$
For $Q = 2$ : $AFC = \frac{150}{2} = 75.00$
For $Q = 3$ : $AFC = \frac{150}{3} = 50.00$
For $Q = 4$ : $AFC = \frac{150}{4} = 37.50$
For $Q = 5$ : $AFC = \frac{150}{5} = 30.00$
For $Q = 6$ : $AFC = \frac{150}{6} = 25.00$
For $Q = 7$ : $AFC = \frac{150}{7} \approx 21.43$

Step 2: Calculate Average Variable Cost (AVC)

The Average Variable Cost (AVC) is calculated using the formula: $AVC = \frac{Variable \, Costs}{Quantity}$ For each quantity, we find:

For $Q = 1$ : $AVC = \frac{15}{1} = 15.00$
For $Q = 2$ : $AVC = \frac{35}{2} = 17.50$
For $Q = 3$ : $AVC = \frac{60}{3} = 20.00$
For $Q = 4$ : $AVC = \frac{90}{4} = 22.50$
For $Q = 5$ : $AVC = \frac{135}{5} = 27.00$
For $Q = 6$ : $AVC = \frac{240}{6} = 40.00$
For $Q = 7$ : $AVC = \frac{480}{7} \approx 68.57$

Step 3: Calculate Average Total Cost (ATC)

The Average Total Cost (ATC) is calculated using the formula: $ATC = \frac{Fixed \, Costs + Variable \, Costs}{Quantity}$ For each quantity, we find:

For $Q = 1$ : $ATC = \frac{150 + 15}{1} = 165.00$
For $Q = 2$ : $ATC = \frac{150 + 35}{2} = 92.50$
For $Q = 3$ : $ATC = \frac{150 + 60}{3} = 70.00$
For $Q = 4$ : $ATC = \frac{150 + 90}{4} = 60.00$
For $Q = 5$ : $ATC = \frac{150 + 135}{5} = 57.00$
For $Q = 6$ : $ATC = \frac{150 + 240}{6} = 65.00$
For $Q = 7$ : $ATC = \frac{150 + 480}{7} \approx 90.00$

Final Answer

The calculated values are:

For $Q = 1$ : $AFC = 150.00, AVC = 15.00, ATC = 165.00$
For $Q = 2$ : $AFC = 75.00, AVC = 17.50, ATC = 92.50$
For $Q = 3$ : $AFC = 50.00, AVC = 20.00, ATC = 70.00$

Thus, the final answers are: $\boxed{AFC = 150.00, AVC = 15.00, ATC = 165.00}$ $\boxed{AFC = 75.00, AVC = 17.50, ATC = 92.50}$ $\boxed{AFC = 50.00, AVC = 20.00, ATC = 70.00}$

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