Diagnose profit drop via mix decomposition

Using the scenarios from the previous question, profit falls in the mixed day despite more tables (25 vs 20) and higher average spend ($36 vs $30). 1) Decompose the change in daily profit into volume effect, spend effect, and mix effect. Use a stepwise counterfactual: (a) Start from baseline (20 tables, $30, no coupons), (b) change only tables to 25, (c) change only spend to $36, (d) finally apply the observed mix (10/25 coupon tables). Quantify each step’s contribution and verify the final profit difference. 2) Attribute the loss primarily to which factor(s) and justify with numbers. 3) Design an experiment to measure cannibalization and long-term value of coupon customers: specify randomization unit (e.g., day-of-week or ZIP-level holdout), treatment(s) (discount depth, commission, minimum spend), primary metric (daily contribution margin), guardrails (utilization, service time), and sample-size or duration assumptions. 4) Propose a diagnostic dashboard: which daily KPIs and derived ratios would you track to prevent this surprise in the future?