Below is a competitive set of hotels in a market. Which hotel has best performed for the fair share of occupancy ?[table]
Hotel | Nb rooms | Nb sales A | 120 | 77 B | 80 | 56 C | 120 | 88 D | 220 | 145
[/table]

Question

BlackTom AI · Accepted Answer

Fair-share performance is measured by comparing each hotel’s share of occupied rooms (sales share) to its share of total rooms (room share). The hotel with the highest ratio (sales share ÷ room share) has best performed versus its fair share.

Step 1 — totals:
- Total rooms = 120 + 80 + 120 + 220 = 540 rooms
- Total sales (occupied rooms) = 77 + 56 + 88 + 145 = 366 occupied rooms

Step 2 — compute room share, sales share, expected (fair) sales, and performance ratio for each hotel.

Hotel A:
- Room share = 120 / 540 = 0.222222 (22.22%)
- Sales share = 77 / 366 ≈ 0.210381 (21.04%)
- Fair (expected) sales = room share × total sales = 0.222222 × 366 = 81.333
- Performance ratio = actual / expected = 77 / 81.333 ≈ 0.9467 (94.7%)

Hotel B:
- Room share = 80 / 540 = 0.148148 (14.81%)
- Sales share = 56 / 366 ≈ 0.153005 (15.30%)
- Fair sales = 0.148148 × 366 = 54.222
- Performance ratio = 56 / 54.222 ≈ 1.0331 (103.3%)

Hotel C:
- Room share = 120 / 540 = 0.222222 (22.22%)
- Sales share = 88 / 366 ≈ 0.240437 (24.04%)
- Fair sales = 0.222222 × 366 = 81.333
- Performance ratio = 88 / 81.333 ≈ 1.08197 (108.2%)

Hotel D:
- Room share = 220 / 540 = 0.407407 (40.74%)
- Sales share = 145 / 366 ≈ 0.396174 (39.62%)
- Fair sales = 0.407407 × 366 = 149.111
- Performance ratio = 145 / 149.111 ≈ 0.9729 (97.3%)

Step 3 — interpret results:
- A ratio > 1 means the hotel captured more occupied rooms than its fair share; ratio < 1 means underperforming.
- Hotel C has the highest performance ratio (≈1.082 or 108.2%), so it best outperformed its fair share.

Why other options are incorrect:
- B slightly overperformed (103.3%) but less than C.
- D and A underperformed relative to their fair shares (97.3% and 94.7% respectively).

Conclusion: Hotel C is the best performer versus fair share. Final answer: c. Hotel C.

Below is a competitive set of hotels in a market. Which hotel has best performed for the fair share of occupancy ?[table] Hotel | Nb rooms | Nb sales A | 120 | 77 B | 80 | 56 C | 120 | 88 D | 220 | 145 [/table]单项选择题

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