Given breakeven sales in units of 41,000 and a unit contribution margin of [tex]$9, how many units must be sold to reach a target operating income of $[/tex]42,300?

A. 380,700
B. 4,700
C. 36,300
D. 45,700



Answer :

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.