Answer :
Let's carefully follow the steps required to determine how many shirts the retailer needs to sell for its total costs to equal its total benefits.
1. Understand the Components:
- Monthly fixed cost: \[tex]$500 - Marginal cost per shirt: \$[/tex]5
- Marginal benefit per shirt: \[tex]$10 2. Define Total Cost and Total Benefit: - Total Cost (TC): This includes the monthly fixed cost plus the cost of producing a certain number of shirts. - Total Benefit (TB): This is the revenue generated from selling a certain number of shirts. 3. Formulate The Equations: - Total Cost (TC): \[ \text{TC} = 500 + 5 \times \text{quantity} \] - Total Benefit (TB): \[ \text{TB} = 10 \times \text{quantity} \] We want to find the quantity where these two are equal: \[ \text{TC} = \text{TB} \] 4. Set Up The Equation: \[ 500 + 5 \times \text{quantity} = 10 \times \text{quantity} \] 5. Solve for Quantity: - First, we will bring all terms involving quantity to one side of the equation: \[ 500 = 10 \times \text{quantity} - 5 \times \text{quantity} \] - Simplify: \[ 500 = 5 \times \text{quantity} \] - Solve for the quantity: \[ \text{quantity} = \frac{500}{5} = 100 \] Thus, the retailer would need to sell 100 shirts to make the total cost equal to the total benefit. By looking at the provided table for verification: \begin{tabular}{|l|l|l|l|} \hline Quantity of shirts sold & Marginal cost & Total cost & Marginal benefit \\ \hline 0 & \$[/tex]0 & \[tex]$500 & \$[/tex]0 \\
\hline 25 & \[tex]$125 & \$[/tex]625 & \[tex]$250 \\ \hline 50 & \$[/tex]250 & \[tex]$750 & \$[/tex]500 \\
\hline 75 & \[tex]$375 & \$[/tex]875 & \[tex]$750 \\ \hline 100 & \$[/tex]500 & \[tex]$1,000 & \$[/tex]1,000 \\
\hline 125 & \[tex]$625 & \$[/tex]1,125 & \[tex]$1,250 \\ \hline \end{tabular} We see that when the quantity is 100, both the total cost (\$[/tex]1,000) and the total benefit (\$1,000) are equal.
Therefore, the correct answer is:
B. 100
1. Understand the Components:
- Monthly fixed cost: \[tex]$500 - Marginal cost per shirt: \$[/tex]5
- Marginal benefit per shirt: \[tex]$10 2. Define Total Cost and Total Benefit: - Total Cost (TC): This includes the monthly fixed cost plus the cost of producing a certain number of shirts. - Total Benefit (TB): This is the revenue generated from selling a certain number of shirts. 3. Formulate The Equations: - Total Cost (TC): \[ \text{TC} = 500 + 5 \times \text{quantity} \] - Total Benefit (TB): \[ \text{TB} = 10 \times \text{quantity} \] We want to find the quantity where these two are equal: \[ \text{TC} = \text{TB} \] 4. Set Up The Equation: \[ 500 + 5 \times \text{quantity} = 10 \times \text{quantity} \] 5. Solve for Quantity: - First, we will bring all terms involving quantity to one side of the equation: \[ 500 = 10 \times \text{quantity} - 5 \times \text{quantity} \] - Simplify: \[ 500 = 5 \times \text{quantity} \] - Solve for the quantity: \[ \text{quantity} = \frac{500}{5} = 100 \] Thus, the retailer would need to sell 100 shirts to make the total cost equal to the total benefit. By looking at the provided table for verification: \begin{tabular}{|l|l|l|l|} \hline Quantity of shirts sold & Marginal cost & Total cost & Marginal benefit \\ \hline 0 & \$[/tex]0 & \[tex]$500 & \$[/tex]0 \\
\hline 25 & \[tex]$125 & \$[/tex]625 & \[tex]$250 \\ \hline 50 & \$[/tex]250 & \[tex]$750 & \$[/tex]500 \\
\hline 75 & \[tex]$375 & \$[/tex]875 & \[tex]$750 \\ \hline 100 & \$[/tex]500 & \[tex]$1,000 & \$[/tex]1,000 \\
\hline 125 & \[tex]$625 & \$[/tex]1,125 & \[tex]$1,250 \\ \hline \end{tabular} We see that when the quantity is 100, both the total cost (\$[/tex]1,000) and the total benefit (\$1,000) are equal.
Therefore, the correct answer is:
B. 100
