To determine the number of shirts the retailer needs to sell for the marginal benefits to exceed the total costs, we will follow these steps:
1. Identify the initial fixed cost: The fixed cost of running the online shop each month is \[tex]$500.
2. Determine the marginal cost and benefit per shirt:
- Marginal cost per shirt is \$[/tex]5.
- Marginal benefit per shirt is \[tex]$10.
3. Calculate the total cost for different quantities of shirts sold:
- Total cost includes the fixed cost plus the marginal cost for each additional shirt sold.
4. Calculate the marginal benefit for different quantities of shirts sold:
- It is found by multiplying the number of shirts sold by the marginal benefit per shirt.
5. Compare the total cost and marginal benefit for different quantities to find the point where the marginal benefit exceeds the total cost.
Let's analyze the table provided:
| Quantity of shirts sold | Marginal cost | Total cost | Marginal benefit |
|-------------------------|---------------|------------|------------------|
| 0 | \$[/tex]0 | \[tex]$500 | \$[/tex]0 |
| 25 | \[tex]$125 | \$[/tex]625 | \[tex]$250 |
| 50 | \$[/tex]250 | \[tex]$750 | \$[/tex]500 |
| 75 | \[tex]$375 | \$[/tex]875 | \[tex]$750 |
| 100 | \$[/tex]500 | \[tex]$1,000 | \$[/tex]1,000 |
| 125 | \[tex]$625 | \$[/tex]1,125 | \[tex]$1,250 |
Now, let's determine where the marginal benefit first exceeds the total cost:
- For 0 shirts: Total cost is \$[/tex]500 and marginal benefit is \[tex]$0.
- For 25 shirts: Total cost is \$[/tex]625 and marginal benefit is \[tex]$250.
- For 50 shirts: Total cost is \$[/tex]750 and marginal benefit is \[tex]$500.
- For 75 shirts: Total cost is \$[/tex]875 and marginal benefit is \[tex]$750.
- For 100 shirts: Total cost is \$[/tex]1,000 and marginal benefit is \[tex]$1,000.
- For 125 shirts: Total cost is \$[/tex]1,125 and marginal benefit is \[tex]$1,250.
From the table, we see that at 125 shirts, the marginal benefit (\$[/tex]1,250) exceeds the total cost (\$1,125).
Therefore, the retailer needs to sell 125 shirts for the marginal benefits to be greater than the total costs.
The correct answer is:
B. 125
