Diagnose profit drop via mix decomposition

Building on the prior question's scenarios, the mixed day shows lower profit even though it has more tables (25 instead of 20) and a higher average spend ($36 instead of $30). 1) Break the daily profit change into a volume effect, a spend effect, and a mix effect. Apply a stepwise counterfactual: (a) begin at baseline (20 tables, $30, no coupons), (b) alter only tables to 25, (c) alter only spend to $36, (d) then apply the observed mix (10 of 25 coupon tables). Quantify the contribution of each step and check that the final profit difference matches. 2) Identify which factor(s) are primarily responsible for the loss and support your attribution with the numbers. 3) Design an experiment to measure cannibalization and the long-term value of coupon customers: specify the randomization unit (for example, a day-of-week or ZIP-level holdout), the treatment(s) (discount depth, commission, minimum spend), the 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 monitor to avoid this kind of surprise going forward? Overview: This question assesses a data scientist's skills in profit decomposition, attribution, experiment design, and diagnostic dashboarding in the Analytics & Experimentation domain.