To determine the number of units that must be sold to reach the target operating income, we need to follow a step-by-step approach:
1. Understand the given data:
- Breakeven sales in units: 41,000 units
- Unit contribution margin: [tex]$9 per unit
- Target operating income: $[/tex]42,300
2. Calculate the number of additional units needed to achieve the target operating income:
- The target operating income must compensate for additional units sold beyond the breakeven point.
- To find the additional number of units needed, we divide the target operating income by the unit contribution margin:
[tex]\[
\text{Units needed} = \frac{\text{Target operating income}}{\text{Unit contribution margin}} = \frac{\$42,300}{\$9/\text{unit}} = 4,700 \text{ units}
\][/tex]
3. Determine the total number of units needed to reach the target operating income:
- The total number of units sold is the sum of the breakeven sales units and the additional units required:
[tex]\[
\text{Total units needed} = \text{Breakeven sales units} + \text{Units needed} = 41,000 \text{ units} + 4,700 \text{ units} = 45,700 \text{ units}
\][/tex]
Given the calculations, the number of units that must be sold to reach a target operating income of $42,300 is:
D. 45,700 units.
