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

A) 120 arrive (and leave) per day

B) a 6.25% increase

Step-by-step explanation:

A) average of 1,200 skiers in LaVilla

they stay on average for 10 days

flow rate = inventory / flow time = 1,200 / 10 = 120

B) If tourists will stay only 5 days instead of 10, 240 tourists will be arriving and leaving every day.

To calculate this we will take any 1 day period:

Scenario 1 (10) old guests new guests total

day 1 1,080 120 1,200

total expenditures $32,400 $6,000 $38,400

Scenario 2 (5) old guests new guests total

day 1 960 240 1,200

total expenditures $28,800 $12,000 $40,800

If the average stay is reduced to 5 days, then the total restaurant revenue should increase by $2,400 or 6.25%.