Question

steven company has fixed costs of $160,000. the unit selling price, variable cost per unit, and contribution margin per unit for the companys two products are as follows:

product | selling price per unit | variable cost per unit | contribution margin per unit
--- | --- | --- | ---
x | $180 | $80 | $100
y | 100 | 50 | 50

the sales mix for products x and y is 60% and 40%, respectively. determine the break-even point in units of x and y. round answers to the nearest whole number.

units of x
units of y

Explanation:

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<reasoning>

Calculate weighted average contribution margin

Using the Sales Mix and Weighted Average Contribution Margin knowledge points
\[

$$\begin{aligned} \text{WACM} &= (\text{CM}_X \times \text{Mix}_X) + (\text{CM}_Y \times \text{Mix}_Y) \\ &= (\$100 \times 0.60) + (\$50 \times 0.40) \\ &= \$60 + \$20 \\ &= \$80 \end{aligned}$$

\]

Determine total break-even units

Using the Fixed Cost and Break-Even Analysis knowledge points
\[

$$\begin{aligned} \text{Total Break-Even Units} &= \frac{\text{Fixed Costs}}{\text{WACM}} \\ &= \frac{\$160,000}{\$80} \\ &= 2,000 \text{ units} \end{aligned}$$

\]

Calculate break-even units for each product

Using the Sales Mix knowledge point
\[

$$\begin{aligned} \text{Units of X} &= 2,000 \times 0.60 = 1,200 \\ \text{Units of Y} &= 2,000 \times 0.40 = 800 \end{aligned}$$

\]
</reasoning>

<answer>
The sales mix for Products X and Y is 60% and 40%, respectively. Determine the break-even point in units of X and Y. Round answers to the nearest whole number.
<blank>1,200</blank> units of X
<blank>800</blank> units of Y
</answer>

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Answer:

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<reasoning>

Calculate weighted average contribution margin

Using the Sales Mix and Weighted Average Contribution Margin knowledge points
\[

$$\begin{aligned} \text{WACM} &= (\text{CM}_X \times \text{Mix}_X) + (\text{CM}_Y \times \text{Mix}_Y) \\ &= (\$100 \times 0.60) + (\$50 \times 0.40) \\ &= \$60 + \$20 \\ &= \$80 \end{aligned}$$

\]

Determine total break-even units

Using the Fixed Cost and Break-Even Analysis knowledge points
\[

$$\begin{aligned} \text{Total Break-Even Units} &= \frac{\text{Fixed Costs}}{\text{WACM}} \\ &= \frac{\$160,000}{\$80} \\ &= 2,000 \text{ units} \end{aligned}$$

\]

Calculate break-even units for each product

Using the Sales Mix knowledge point
\[

$$\begin{aligned} \text{Units of X} &= 2,000 \times 0.60 = 1,200 \\ \text{Units of Y} &= 2,000 \times 0.40 = 800 \end{aligned}$$

\]
</reasoning>

<answer>
The sales mix for Products X and Y is 60% and 40%, respectively. Determine the break-even point in units of X and Y. Round answers to the nearest whole number.
<blank>1,200</blank> units of X
<blank>800</blank> units of Y
</answer>

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