Question

(LaVilla) LaVilla is a village in the Italian Alps. Given its enormous popularity among

Swiss, German, Austrian, and Italian skiers, all of its beds are always booked in the winter
season and there are, on average, 1,200 skiers in the village. On average, skiers stay in
LaVilla for 10 days.
a. How many new skiers are arriving—on average—in LaVilla every day?
b. A study done by the largest hotel in the village has shown that skiers spend on average $50 per person on the first day and $30 per person on each additional day in local
restaurants. The study also forecasts that—due to increased hotel prices—the average
length of stay for the 2003/2004 season will be reduced to five days. What will be the
percentage change in revenues of local restaurants compared to last year (when skiers
still stayed for 10 days)? Assume that hotels continue to be fully booked!
Q2.6 (Highway) While driving home for the holidays, you can’t seem to get Little’s Law out of

Answer 1

a) 120 skiers per day

b) 6.25% increase in revenue

Step-by-step explanation:

a) If the average skier stays 10 days, the average turnover is 1/10 of the skiers per day, or 1200/10 = 120 skiers per day.

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b) For a stay of n days, the average skier spends ...

50 +(n-1)30 = 20 +30n

and the average spending per day is ...

(20 +30n)/n = (20/n) +30

So, for a 10-day stay, the average skier spends in restaurants ...

20/10 +30 = 32 . . . . per day

And for a 5-day stay, the average skier will spend ...

20/5 +30 = 34 . . . . per day

The change in restaurant revenue is expected to be ...

(34 -32)/32 × 100% = 2/32 × 100% = 6.25%

Restaurant revenues will be 6.25% higher compared to last year.