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This is the break-even volume at the product sales mix, although the volumes for the two products are reversed. But even if the reversal were corrected, this would not be the correct answer because this is for the current product sales mix, not the expected sales mix.
This is the break-even volume at the current product sales mix of round and heart-shaped cakes. If the product sales mix changes to three heart-shaped cakes for each round cake, the breakeven volume for the two cakes will be different.
The contribution margin for round cakes is $4 ($12 ? $8). The contribution margin for heart-shaped cakes is $5 ($20 ? $15). If three heart-shaped cakes are sold for each 1 round cake, the heart-shaped cakes will represent 75% of sales and round cakes will represent 25% of sales. The unit contribution margin is a weighted average of the contribution margins of the two different cakes, weighted according to their percentages of sales. That is: (.25 × $4) + (.75 × $5) = $4.75. The break-even volume in total number of units is the fixed cost of $94,000 divided by the weighted average unit contribution margin of $4.75, which is 19,789.47 units. This 19,789.47 units is split between heart-shaped cakes and round cakes at the ratio of 75% heart-shaped cakes and 25% round cakes. Therefore, the number of each type of cake to break even at this product mix is: Round cakes: 19,789.47 × .25 = 4,947.34 or 4,948 (since a partial cake cannot be sold); and ?Heart-shaped cakes: 19,789.47 × .75 = 14,842.10, or 14,843.
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