Use this information for Rusty Co. to answer the questions that follow.

Rusty Co. sells two products, X and Y. Last year, Rusty sold 5,000 units of X and 35,000 units of Y. Related data are as follows:

Unit Selling Price

Unit Variable

Unit Contribution

Product

Price

Cost

Margin

X

$110

$70

$40

Y

70

50

20

Assuming that last year’s fixed costs totaled $675,000, what was Rusty Co.’s break-even point in sales units? Do not round interim computations.

Question

Use this information for Rusty Co. to answer the questions that follow.

​

Rusty Co. sells two products, X and Y. Last year, Rusty sold 5,000 units of X and 35,000 units of Y. Related data are as follows:

Unit Selling Price

Unit Variable

Unit Contribution

Product

Price

Cost

Margin

X

$110

$70

$40

Y

70

50

20

​

Assuming that last year’s fixed costs totaled $675,000, what was Rusty Co.’s break-even point in sales units? Do not round interim computations.

BlackTom AI · Accepted Answer

Weighted-average contribution margin per unit equals the key to a multi-product break-even in units.

1) Relevant concepts:
- Contribution margin (CM) per unit = Selling price − Variable cost.
- For multiple products sold in a constant sales mix, compute the weighted-average CM per unit using the mix proportions, then divide fixed costs by that weighted CM to get break-even units.

2) Step-by-step reasoning and intermediate calculations:
- Compute sales mix (units sold last year): X = 5,000; Y = 35,000; total = 40,000 units.
- Mix proportions: X = 5,000/40,000 = 0.125 (12.5%); Y = 35,000/40,000 = 0.875 (87.5%).
- Contribution margin per unit (given): CM_X = $40; CM_Y = $20.
- Weighted-average CM per unit = (0.125 × $40) + (0.875 × $20)
  = $5.00 + $17.50
  = $22.50 per unit.
- Fixed costs = $675,000. Break-even units (in the given mix) = Fixed costs / Weighted-average CM
  = $675,000 / $22.50
  = 30,000 units.

3) Why the correct answer is correct:
Using the firm’s actual selling mix ensures each unit of the composite mix contributes $22.50 toward fixed costs. Dividing total fixed costs by $22.50 yields the number of mixed units required to cover fixed costs—30,000 units—so at that volume total contribution equals fixed costs and net operating income is zero.

4) Why the other choices are incorrect:
- 16,875 units = $675,000 / $40 (this treats the entire mix as product X only, ignoring product Y and the actual mix).
- 11,250 units = $675,000 / $60 (this would correspond to an incorrect CM value of $60; not applicable).
- 30,100 units is a rounding or arithmetic error; the exact computation gives 30,000 units.

Conclusion: The break-even point in sales units is 30,000 units, which matches the provided correct answer.

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