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}
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Solution

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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:

  1. Average Fixed Cost (AFC) = Fixed Costs / Quantity
  2. Average Variable Cost (AVC) = Variable Costs / Quantity
  3. 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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