Breakeven Analysis: How Many Scans Does Seattle Radiology Group Need for Scanner B?

To calculate the breakeven volume for Scanner B, we need to determine the number of scans at which the group will neither make a profit nor incur a loss.

Let's assume the breakeven volume is x scans.

At the breakeven volume, the total revenue will be equal to the total costs.

Total revenue = Total fixed costs + Total variable costs

Total revenue = $800,000 + ($1,500 * x)

Total costs = $800,000 + ($1,500 * x)

Profit = Total revenue - Total costs

At a volume of 5,000 scans, the profit is $450,000.

$450,000 = $800,000 + ($1,500 * 5,000)

$450,000 = $800,000 + $7,500,000

$7,950,000 = $800,000 + $1,500 * x

$1,500 * x = $7,950,000 - $800,000

$1,500 * x = $7,150,000

x = $7,150,000 / $1,500

x = 4,766.67

Therefore, the estimated breakeven volume for Scanner B is approximately 4,767 scans.

Among the given options, the closest option is 5,000.