Current Attempt in Progress
Wildhorse Corporation sells three different models of a mosquito “zapper.” Model A12 sells for and has
unit variable costs of . Model B22 sells for and has unit variable costs of . Model C124
sells for and has unit variable costs of . The sales mix (as a percentage of total units) of the three
models is A12, 60%; B22, 15%; and C124, 25%.
If the company has fixed costs of , how many units of each model must the company sell in order to
break even? (Round Per unit values to 2 decimal palces, e.g. 15.25 and final answers to 0 decimal
places, e.g. 5,275.)
Model
A12
B22
C124
Total break-even point

Ask by Savage Mullins. in the United States

Mar 15,2025

Question

Current Attempt in Progress
Wildhorse Corporation sells three different models of a mosquito “zapper.” Model A12 sells for and has
unit variable costs of . Model B22 sells for and has unit variable costs of . Model C124
sells for and has unit variable costs of . The sales mix (as a percentage of total units) of the three
models is A12, 60%; B22, 15%; and C124, 25%.
If the company has fixed costs of , how many units of each model must the company sell in order to
break even? (Round Per unit values to 2 decimal palces, e.g. 15.25 and final answers to 0 decimal
places, e.g. 5,275.)
Model
A12
B22
C124
Total break-even point

Ask by Savage Mullins. in the United States

Mar 15,2025

UpStudy AI · Accepted Answer

Let

$$
x = \text{total weighted units sold at break‐even.}
$$

For each model, we first calculate the contribution margin per unit.

Model A12:  
$$
\text{Selling price} = \$61,\quad \text{Variable cost} = \$42.70
$$
$$
\text{Contribution margin} = 61 - 42.70 = 18.30
$$

Model B22:  
$$
\text{Selling price} = \$122,\quad \text{Variable cost} = \$85.40
$$
$$
\text{Contribution margin} = 122 - 85.40 = 36.60
$$

Model C124:  
$$
\text{Selling price} = \$488,\quad \text{Variable cost} = \$366
$$
$$
\text{Contribution margin} = 488 - 366 = 122.00
$$

The sales mix (as a percentage of total units sold) for each model is as follows:

- Model A12: 60\%  
- Model B22: 15\%  
- Model C124: 25\%

The weighted average contribution margin per unit is computed as

$$
\text{CM}_{\text{avg}} = 0.60(18.30) + 0.15(36.60) + 0.25(122.00)
$$

Calculating each term:

$$
0.60(18.30) = 10.98
$$
$$
0.15(36.60) = 5.49
$$
$$
0.25(122.00) = 30.50
$$

Thus,

$$
\text{CM}_{\text{avg}} = 10.98 + 5.49 + 30.50 = 46.97
$$

The break‐even point in weighted units is given by

$$
x = \frac{\text{Fixed Costs}}{\text{CM}_{\text{avg}}} = \frac{267729}{46.97} \approx 5700.00
$$

Now, the break‐even quantity for each model is determined by applying the sales mix:

Model A12:

$$
\text{Units of A12} = 0.60 \times 5700 = 3420.00 \quad (\text{rounded to } 3420)
$$

Model B22:

$$
\text{Units of B22} = 0.15 \times 5700 = 855.00 \quad (\text{rounded to } 855)
$$

Model C124:

$$
\text{Units of C124} = 0.25 \times 5700 = 1425.00 \quad (\text{rounded to } 1425)
$$

Thus, the company must sell

- $$\textbf{3420}$$ units of Model A12,
- $$\textbf{855}$$ units of Model B22, and
- $$\textbf{1425}$$ units of Model C124

to break even with a total of $$\textbf{5700}$$ weighted units.
To break even, Wildhorse Corporation must sell: - **3,420** units of Model A12, - **855** units of Model B22, and - **1,425** units of Model C124. This totals **5,700** weighted units.

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