Answer (A) is correct . In a multiproduct setting, the contribution margin of each product must be weighted according to its proportion of total sales. Specialty’s breakeven quantities can therefore be derived thusly: ? Weighted UCM = {($12 – $8) × [10,000 ÷ (10,000 + 15,000)]} + {($20 – $15) × [15,000 ÷ (10,000 + 15,000)]} = ($4 × 40%) + ($5 × 60%) = $1.60 + $3.00 = $4.60 per composite unit Breakeven point = Fixed costs ÷ UCM = $92,000 ÷ $4.60 = 20,000 composite units The breakeven point in round cakes is therefore 8,000 units (20,000 composite × 40%), and the breakeven point in heart-shaped cakes is 12,000 units (20,000 composite × 60%).
Answer (B) is incorrect because An allocation of 9,000 round cakes and 11,000 heart-shaped cakes results from an improper weighting of 55:45.
Answer (C) is incorrect because An allocation of 10,000 round cakes and 10,000 heart-shaped cakes results from an improper weighting of 50:50.
Answer (D) is incorrect because An allocation of 23,000 round cakes and 18,400 heart-shaped cakes results from assuming $184,000 of fixed costs ($92,000 for each product) and calculating the breakeven point for each cake separately.
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How many cakes will be required to reach the breakeven point?