Compute profit and decompose Groupon impact

Q: Compute profit and decompose Groupon impact

This question evaluates quantitative reasoning in profit accounting, margin calculations, and impact decomposition for promotional interventions such as coupon commissions, relevant for a Data Scientist assessing business metrics.

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Question

You run a restaurant with these economics: baseline demand is 20 tables/day, average revenue is $30/table, variable cost (VC) is 40% of revenue, and fixed cost (FC) is$ 100/day. A Groupon-like site proposes that when a table uses a coupon, you pay a 40% commission on that table’s check (max one coupon per table). Answer the following: (a) What is your baseline daily profit? (b) If all 20 tables used a coupon and the table count stayed at 20/day, what average check per table would keep your daily profit equal to baseline? (c) After joining, you observe 25 tables/day; 10 tables present a coupon; the overall average check (across all 25 tables) is $36; VC and FC are unchanged. What is your new daily profit? Show the arithmetic and decompose the profit delta vs baseline into three labeled components: (i) change in table count, (ii) change in average check, (iii) commissions on coupon tables. (d) Based solely on the numbers in (c), is profit up or down vs baseline? By how much, and what is the primary driver?

Compute profit and decompose Groupon impact

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