Chapter 24 — Self-Check Quiz

Revenue Management: Covers, Seat Turns, RevPASH, and Pricing the Room

Twenty-five questions. Answer key at the bottom. Do the arithmetic on paper before you look.

Bellwether reference figures: 68 seats, dinner 5:00–10:00 Tue–Sat (62 / 78 / 92 / 120 / 123 covers), brunch 10:00–2:00 Sat–Sun (110 covers each), \$46 dinner check, \$24 brunch check, 95-minute dinner dine time, 70-minute brunch dine time.

Multiple choice

1. RevPASH is best defined as:

  • A. Revenue divided by covers served
  • B. Revenue divided by available seats multiplied by hours open
  • C. Revenue divided by occupied seat-hours
  • D. Revenue divided by seats, per service

2. A restaurant's RevPASH rises while its cover count falls. The most likely explanation is:

  • A. Capacity utilization improved
  • B. Average check rose, dine time fell, or both
  • C. The restaurant added seats
  • D. The service window lengthened

3. Bellwether's dinner service manufactures how many seat-hours?

  • A. 68 per service
  • B. 340 per service
  • C. 475 per service
  • D. 1,700 per service

4. Which of these is not one of the three levers RevPASH decomposes into?

  • A. Capacity utilization
  • B. Average check
  • C. Average dine time
  • D. Seat turns

5. A fence, in revenue-management terms, is:

  • A. A cap on how many discounted covers you will sell
  • B. A restriction that prevents a full-price guest from accessing the discounted price
  • C. A minimum spend requirement
  • D. A physical barrier between dining areas

6. Bellwether's Saturday dinner is 57.3% capacity utilization. This means:

  • A. 57.3% of tables were occupied at peak
  • B. 57.3% of reservations were honored
  • C. Occupied seat-hours were 57.3% of available seat-hours
  • D. The restaurant hit 57.3% of its revenue target

7. Which pair of Bellwether services consumes exactly the same number of available seat-hours?

  • A. Saturday dinner and Saturday brunch
  • B. Tuesday plus Wednesday dinner, and Friday plus Saturday dinner
  • C. Both brunches, and Friday dinner
  • D. Thursday dinner and both brunches combined

8. An unfenced 20%-off promotion aimed at a slow Tuesday most commonly:

  • A. Fills Tuesday and pays for itself in beverage
  • B. Is claimed mostly by guests who were already coming on the busy nights
  • C. Attracts new guests who convert to full-price regulars
  • D. Raises RevPASH on Tuesday by about 20%

9. A prix fixe cover at Bellwether contributes \$29.87 over 75 minutes; an à la carte cover contributes \$33.23 over 95 minutes. On contribution per occupied seat-hour:

  • A. À la carte wins by roughly \$3
  • B. They are equal
  • C. Prix fixe wins by roughly \$3
  • D. It cannot be determined without the food cost

10. Duration management converts into revenue only when:

  • A. The kitchen has spare capacity
  • B. There is demand for the seat you freed
  • C. The average check is above \$40
  • D. Labor is scheduled to a productivity standard

11. Bellwether's binding constraint on a Saturday at 7:45 p.m. is:

  • A. Available seats
  • B. Server capacity
  • C. The hearth's sustainable rate of 28 items an hour
  • D. Bar throughput

12. Which no-show policy design is correct according to the chapter?

  • A. Charge for no-shows and for cancellations inside 24 hours, on all bookings
  • B. Charge for no-shows only in the peak window; make cancellation free and easy
  • C. Require full prepayment on all Friday and Saturday bookings
  • D. Charge nothing and absorb the loss as a cost of hospitality

13. Adding Bellwether's patio to the plan changes on-premise RevPASH from \$12.09 to \$11.60. This tells you:

  • A. The patio is unprofitable and should be cut
  • B. RevPASH is a comparison metric, not an objective function
  • C. The patio's check average is too low
  • D. The seat-hour calculation is wrong

14. Bellwether's dining room is short which table type?

  • A. Two-tops
  • B. Four-tops
  • C. Six-tops
  • D. Bar seats

15. A \$3,000 four-hour buyout is a good deal on a Monday and a poor one on a Friday because:

  • A. Monday labor is cheaper
  • B. Friday food cost is higher
  • C. The seat-hours it consumes have different opportunity value
  • D. Weekend guests tip better

Short answer

16. Bellwether's Saturday brunch does 110 covers and Tuesday dinner does 62. Which service produces more revenue, by how much, and what does that tell you about managing by cover count?

17. Write the RevPASH formula and the three-lever decomposition, and verify Bellwether's dinner week ( \$12.85 ) from the decomposition.

18. Name the three fences available to a restaurant and give Bellwether's early prix fixe as an example using all three.

19. Why does the chapter say a peak surcharge and an off-peak discount of the same size are "financially identical and operationally opposite"?

20. Explain, in two sentences, why an incremental Tuesday cover is worth more to Bellwether than an incremental Friday cover, even though both carry a \$46 check.

21. A four-top seated with two guests destroys 3.5 seat-hours. Under what condition is the dollar cost of that zero, and under what condition is it \$92?

22. What does Chapter 14's finding that "wave-splitting creates zero capacity" rule out, and what does it not rule out?

23. Bellwether's revenue bridge is \$139,240. State its five components and their builds, and say what fraction of the bridge this chapter owns.

24. Give the chapter's test for whether a demand-based pricing instrument is defensible, and name the case the test handles badly.

25. A 60-seat restaurant runs 2.4 seat turns on a Saturday across a five-hour service with a 55-minute average dine time. Compute capacity utilization and say what the two numbers together should make you check.

Answer key **1. B.** Revenue ÷ (available seats × hours open). Option C is *revenue per occupied seat-hour*, a useful diagnostic but a different number — it deliberately excludes the empty seats that make the inventory perishable in the first place. **2. B.** Both live in the revenue-per-occupied-seat-hour term. If covers fell, utilization almost certainly fell too, so the gain has to have come from a higher check, a shorter dine time, or both. **3. B.** 68 seats × 5 hours = **340 seat-hours per dinner service**; 1,700 across the five-night dinner week. **4. D.** Seat turns is a separate (and cruder) metric. The three levers are utilization, average check, and average dine time. **5. B.** A fence is what makes a discount an instrument rather than a price cut. **6. C.** Occupied seat-hours ÷ available seat-hours: $123 \times 1.583 = 195$ occupied against 340 available. **7. B.** Two dinner services is 680 available seat-hours either way. Tuesday plus Wednesday returns \$6,440; Friday plus Saturday returns \$11,178 — identical inventory, 58 cents on the dollar. **8. B.** Your social-media followers are your regulars, and your regulars come on the busy nights. The people who do not go out on Tuesday are generally busy rather than price-sensitive. **9. C.** $\$29.87 \div 1.25 = \$23.90$ against $\$33.23 \div 1.583 = \$20.99$ — the prix fixe wins by \$2.91 an hour while losing \$3.36 a cover. **10. B.** A shorter dine time with nobody waiting produces an emptier room, which is worth nothing. **11. C.** Utilization peaks at 87% of seats but the hearth is being asked for 32 items an hour against a rated 28 between roughly 7:20 and 9:20. **12. B.** A cancellation returns sellable inventory; a no-show does not. Charging for both teaches guests to go silent, which makes the problem worse. **13. B.** The patio's seat-hours are cheap and sell at a lower rate, so they dilute the average while adding revenue and contribution. Managing to maximize RevPASH would tell you to close it, which is why RevPASH is a comparison tool and not a target to optimize. **14. A.** 17 seatings a night want a two-top; 8 two-tops at 1.71 seatings supply 13.7. **15. C.** On Monday the room is dark and the seat-hours are worth zero, so \$3,000 is \$11.03 of RevPASH against nothing. On Friday the same hours were going to produce \$5,520. **16.** **Tuesday dinner produces more: \$2,852 against \$2,640 — \$212 more on 48 fewer covers.** Brunch does 77% more people and less money. A cover count measures traffic; it says nothing about what the traffic paid or how long it occupied the asset, which is why managing by covers will lead you to praise the wrong service and starve the right one. **17.** $\text{RevPASH} = \text{Revenue} \div (\text{available seats} \times \text{hours open})$, and $\text{RevPASH} = \text{utilization} \times (\text{average check} \div \text{average dine time in hours})$. Verification: $44.2\% \times (\$46.00 \div 1.583) = 0.442 \times \$29.05 = \mathbf{\$12.85}$. Direct: $\$21{,}850 \div 1{,}700 = \$12.85$. They agree. **18.** **Time** (5:00–6:15 seatings only), **day** (Tuesday and Wednesday only), and **product** (three fixed courses, quarter-portion Hearth Chicken, no substitutions). All three at once, which is standard: a Saturday 7:30 guest who wants the full-size chicken has no path to \$34. **19.** Because the algebra is symmetric and loss aversion is not. Set the base price at \$58 and discount to \$46, or set it at \$46 and surcharge to \$58 — the spread and the revenue are the same. One reads as a gift and one reads as a penalty, and guests respond to the framing rather than the arithmetic. Hence the rule: **discount the trough, never surcharge the peak.** **20.** The Tuesday crew is a fixed labor floor that is being paid regardless, so an incremental Tuesday cover contributes very close to the full \$33.23 with no additional labor. An incremental Friday cover needs an incremental server hour, competes for a table someone is waiting for, and lands on a hearth already over its rate. **21.** Zero when nobody wanted those seats — a Tuesday at 7:10 with a 29%-full room and no wait. \$92 (two covers at \$46) when there is a wait at the door, i.e. Friday and Saturday between roughly 6:45 and 8:45. **22.** It rules out the belief that splitting the same covers into two seatings makes the hearth produce more — it does not; the rate is 28 items an hour whatever the reservation grid says. It does *not* rule out reshaping the arrival curve, which adds no capacity but uses more of the capacity already owned, by moving load out of the hours that are over rate into the hours running at eleven items. **23.** Patio dinner (100 services × 12 incremental covers × \$46 = \$55,200); patio brunch (40 services × 10 covers × \$24 = \$9,600); private events (14 × \$3,000 = \$42,000, Chapter 29); takeout (52 weeks × \$600 = \$31,200, Chapter 28); forfeited deposits (62 seats × \$20 = \$1,240, §24.7). This chapter owns the patio and the deposits — **\$66,040, or 47%**. The other 53% belongs to Chapters 28 and 29. **24.** *Can the guest see the rule and choose the cheaper side of it?* Posted, predictable, choosable differentials pass; opaque, individualized, or undisclosed ones fail. The test handles badly the guest who genuinely cannot choose the cheap side — someone who works every Tuesday evening pays more for being unavailable, and being unavailable is not a moral failing. The chapter does not claim to resolve that. **25.** Occupied seat-hours: $60 \times 2.4 = 144$ covers × $(55 \div 60) = 132$ occupied against $60 \times 5 = 300$ available — **44% capacity utilization.** So a very impressive-sounding turns figure sits on a room that is 56% empty by the seat-hour, because the dine time is unusually short. Before congratulating anyone, check whether 55 minutes is the concept (fast, counter-adjacent, high-volume) or the symptom (guests being moved along) — and check the second-visit rate, because a rushed dinner shows up in Chapter 23's numbers long before it shows up here.