Answer :
To determine how many shirts the retailer needs to sell for its marginal benefits to be greater than its total costs, we need to analyze the provided table.
Let's break down the components:
1. Fixed Cost: The retailer has a fixed cost of \[tex]$500 per month. 2. Marginal Cost per Shirt: The cost of acquiring one shirt is \$[/tex]5.
3. Marginal Benefit per Shirt: The revenue from selling one shirt is \[tex]$10. Now, using the information given in the table, let's calculate the Marginal Cost, Total Cost, and Marginal Benefit for different quantities of shirts sold: \[ \begin{array}{|l|l|l|l|} \hline \text{Quantity of shirts sold} & \text{Marginal cost} & \text{Total cost} & \text{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 & \[tex]$1,250 \\ \hline \end{array} \] To find the answer, we need to compare the Marginal Benefit with the Total Cost for each quantity of shirts sold: - At 0 shirts sold: Marginal Benefit (\$[/tex]0) < Total Cost (\[tex]$500) - At 25 shirts sold: Marginal Benefit (\$[/tex]250) < Total Cost (\[tex]$625) - At 50 shirts sold: Marginal Benefit (\$[/tex]500) < Total Cost (\[tex]$750) - At 75 shirts sold: Marginal Benefit (\$[/tex]750) < Total Cost (\[tex]$875) - At 100 shirts sold: Marginal Benefit (\$[/tex]1,000) = Total Cost (\[tex]$1,000) - At 125 shirts sold: Marginal Benefit (\$[/tex]1,250) > Total Cost (\$1,125)
From the comparison above, the Marginal Benefit first exceeds the Total Cost when 125 shirts are sold.
So, the retailer would need to sell 125 shirts for its marginal benefits to be greater than its total costs.
Thus, the correct answer is:
B. 125
Let's break down the components:
1. Fixed Cost: The retailer has a fixed cost of \[tex]$500 per month. 2. Marginal Cost per Shirt: The cost of acquiring one shirt is \$[/tex]5.
3. Marginal Benefit per Shirt: The revenue from selling one shirt is \[tex]$10. Now, using the information given in the table, let's calculate the Marginal Cost, Total Cost, and Marginal Benefit for different quantities of shirts sold: \[ \begin{array}{|l|l|l|l|} \hline \text{Quantity of shirts sold} & \text{Marginal cost} & \text{Total cost} & \text{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 & \[tex]$1,250 \\ \hline \end{array} \] To find the answer, we need to compare the Marginal Benefit with the Total Cost for each quantity of shirts sold: - At 0 shirts sold: Marginal Benefit (\$[/tex]0) < Total Cost (\[tex]$500) - At 25 shirts sold: Marginal Benefit (\$[/tex]250) < Total Cost (\[tex]$625) - At 50 shirts sold: Marginal Benefit (\$[/tex]500) < Total Cost (\[tex]$750) - At 75 shirts sold: Marginal Benefit (\$[/tex]750) < Total Cost (\[tex]$875) - At 100 shirts sold: Marginal Benefit (\$[/tex]1,000) = Total Cost (\[tex]$1,000) - At 125 shirts sold: Marginal Benefit (\$[/tex]1,250) > Total Cost (\$1,125)
From the comparison above, the Marginal Benefit first exceeds the Total Cost when 125 shirts are sold.
So, the retailer would need to sell 125 shirts for its marginal benefits to be greater than its total costs.
Thus, the correct answer is:
B. 125
