To find the number of units of each product sold at the breakeven point, follow these steps:
1. Identify the given information:
- Fixed costs = [tex]$1,080,000
- Weighted-average contribution margin per unit = $[/tex]135
- Sales mix: 60% tablets and 40% smartphones
2. Calculate the total number of units needed to cover the fixed costs at the breakeven point:
The formula for the breakeven point in units is:
[tex]\[
\text{Total units at breakeven} = \frac{\text{Fixed costs}}{\text{Weighted-average contribution margin per unit}}
\][/tex]
Substituting the given values:
[tex]\[
\text{Total units at breakeven} = \frac{1,080,000}{135} = 8,000 \text{ units}
\][/tex]
3. Determine the units of each product at the breakeven point based on the sales mix:
Since 60% of the sales are tablets and 40% are smartphones, we divide the total breakeven units according to these percentages.
- Units of tablets:
[tex]\[
\text{Units of tablets} = 8,000 \times 0.60 = 4,800 \text{ units}
\][/tex]
- Units of smartphones:
[tex]\[
\text{Units of smartphones} = 8,000 \times 0.40 = 3,200 \text{ units}
\][/tex]
4. Summary:
- Total units at breakeven point: 8,000 units
- Units of tablets at breakeven point: 4,800 units
- Units of smartphones at breakeven point: 3,200 units
Therefore, at the breakeven point, US-Mobile needs to sell 4,800 units of tablets and 3,200 units of smartphones to cover the fixed costs of $1,080,000.
