Compute Groupon unit economics and break-even

Question

You operate a restaurant with the following daily economics:

• Baseline demand: 20 tables/day (assume one party per table)
• Average pre-discount spend: $30/table
• Variable cost (VC): 40% of pre-discount spend
• Fixed cost (FC): $100/day
• Disregard tips and taxes

A daily-deal platform like Groupon offers this voucher: a customer pays $15 for a voucher worth $30 of food, and the platform keeps a 40% commission on the $15 the customer pays. Only one voucher may be used per table. Let n be a table's total pre-discount spend when a voucher is redeemed. For each part, show your formulas and final numbers.

1. Baseline profit. What daily profit do you earn before joining the deal site?
2. Break-even on a voucher table. Using the unit-economics model $Revenue = n$ and $Costs = 0.4n + \$15 \text{ (face value the customer redeems)} + 0.4 \times \$15 \text{ (the site's commission)}$, solve for the break-even n at which a voucher table contributes zero profit.
3. All tables on vouchers. If all 20 tables used a voucher and the daily table count stayed at 20, what average pre-discount spend per table would keep daily profit equal to the baseline?
4. Mixed day. After joining, you observe 25 tables/day; 10 of them present a voucher; the average pre-discount spend across all 25 tables is $36; VC and FC are unchanged. What is the new daily profit?
5. Decomposition. Break the profit change versus baseline into three labeled components: (i) change in table count, (ii) change in average spend per table, (iii) voucher cost on the coupon tables (face value plus commission). Is profit up or down versus baseline, by how much, and what is the primary driver?
6. Sensitivity. Holding regular tables at $36 and both counts unchanged, what minimum average pre-discount spend per coupon table makes daily profit equal to the baseline in part 1?

Overview: This is a Capital One data science technical screen case on restaurant unit economics with a Groupon-style voucher. You compute baseline daily profit from a 20-table day, derive the break-even check for a voucher table under a $30-for-$15 offer with a 40% commission, profit a mixed 25-table day, and decompose the profit change into traffic, check size and voucher cost. It includes full worked arithmetic, a sensitivity solve, and the incrementality follow-ups an interviewer expects.