# Evaluate Two Partnerships with Unit Economics and Break-Even Analysis Work through two profitability cases. In the first, a restaurant considers a discount-platform partnership and different prescription-style service tiers have different costs. In the second, a payments product offers a profitable credit option and a loss-making debit option. ### Constraints & Assumptions - Use variables when a numerical input is not supplied; do not assume hidden source numbers. - Separate revenue, variable cost, fixed cost, and one-time cost. - State whether customer counts are incremental or cannibalized from an existing channel. - A recommendation must include sensitivity analysis, not only a point estimate. ### Clarifying Questions to Ask - Does the partnership fee apply to gross sales, discounted sales, or each transaction? - Which costs vary by customer, tier, or payment product? - Is break-even measured per day, per customer cohort, or over the contract term? ### Part 1 — Restaurant partnership Build the daily profit equation before and after the partnership, derive break-even volume, and derive the mix of low-cost and high-cost service tiers required to hold profit constant. #### What This Part Should Cover - A complete profit equation - A symbolic break-even derivation - An expected-cost equation for the tier mix ### Part 2 — Credit and debit products Given current losses and the incremental contribution margin of one additional customer, derive the customers needed to break even. Explain how you would judge whether the result is operationally realistic. #### What This Part Should Cover - Contribution margin per incremental customer - A denominator and units check - Changes to pricing, cost, or product mix if acquisition alone is unrealistic ### What a Strong Answer Covers - Transparent arithmetic and units - Clear incremental-versus-existing assumptions - A recommendation robust to plausible ranges ```hint Write the equation before substituting Name every revenue and expense term and its unit. This prevents mixing per-order margins with daily fixed costs or treating existing customers as incremental. ``` ### Follow-up Questions - How would cannibalization change the recommendation? - Which uncertain input has the highest value of information?