Question

This question is about a ski lift at a ski resort. Each seat can hold 4 people and seats depart once every 15 seconds. People arrive at random with an average rate of 15 people per minute. People are complaining that the lift is often busy and they have to wait for a free seat to take them up the mountain. You’re considering two options for ensuring faster service:

- Speeding up the motor and lift equipment at a cost of $190,000 so that seats that can hold 4 people depart once every 12 seconds;

- or installing wider seats that can hold 5 people each, at a cost of $270,000. (Seats depart once every 15 seconds.)

You decide to base your decision on the number of customers who arrive during the time you can serve them. You don’t want to have more than a 0.2 probability of more customers arriving than you can serve. For instance, with your current operation, you can serve 4 customers in 15 seconds, so you don’t want the probability of more than 4 customers arriving in 15 seconds to be greater than 20%.

Calculate the probabilities of more customers arriving than you can serve for each of the three scenarios:

(i) continue the current operation,

(ii) upgrade the motor and lift equipment, and

(iii) install wider seats.

Do you need to consider doing both (ii) and (iii) (so that seats holding 5 people depart once every 12 seconds)?

Which option should you choose?

Answer 1