Question

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 2014/2015 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!

Answer 1

Part A:

We can use Little's law to compute average number of skiers

Little Law say, \(L=\lambda W\)

\(\mathrm{L}=\) Average number of skiers

\(\lambda=\) Effective arrival rate

\(W=\) Average time skier spend

Here, \(L=1200, W=10\) days

Thus, Arrival rate = 120 skiers/day

Part B:

Revenue when skiers stayed for 10 days can be computed as:

Spend by 1 skier in 10 days \(=50+30 * 9=320 \$\)

Spend by 1 skier/day \(=320 / 10=32 \$\)

Revenue when skiers stayed for 5 days can be computed as:

Spend by 1 skier in 5 days \(=50+30^{*} 4=170 \$\)

Spend by 1 skier/day \(=170 / 4=34 \$\)

Thus, Revenue \(\%\) differnce \(=(34-32) / 32 * 100=6.25 \%\)

Thus, Revenue will increase by \(6.25 \%\)