Decision Rule: Offer Classic and Vegan Burgers Concurrently?
Context
You are evaluating whether a burger chain should sell a vegan burger alongside the classic burger. You have unit economics (price and variable cost per unit) for both items. When both are offered, demand tends to split approximately 2 vegan : 3 classic by units. Offering the vegan item may entail incremental fixed costs (e.g., equipment/training), and the kitchen has a finite capacity per period (e.g., per day).
Assume:
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Contribution margins: CM_c = p_c − v_c (classic), CM_v = p_v − v_v (vegan).
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Mix when both offered: 2 vegan : 3 classic.
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Cannibalization rate k: share of vegan buyers who would have bought classic if vegan were unavailable (0 ≤ k ≤ 1).
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Capacity C (units/period) and baseline classic-only demand Q0 (units/period).
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Incremental fixed costs to add vegan: ΔF ≥ 0.
Task
Propose a quantitative decision rule for launching both items that explicitly incorporates:
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Contribution margin
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Cannibalization rate thresholds
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Kitchen capacity utilization
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Fixed-cost recovery
Also state the minimal incrementality (net-new units, ΔQ) required for the dual-offer to strictly dominate the classic-only scenario.