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# Buying more elevators

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Posted 25 March 2014 - 02:38 PM

There is a building with 50 floors.  Every morning 100 guest, 2 on each floor, come to use a single elevator.  The elevator has a max capacity of 10 users.  The elevator begins on the 50th floor and travels down.  Once the elevator achieves maximum capacity, the elevator travels only one additional floor.  At this floor, everyone on the elevator exits and those waiting (who have not yet ridden in the elevator) get on the elevator, then the elevator continues with only these new riders.  Everyone above the 1st floor desires to make it to the first floor while those on the first floor wish to make it to the fiftieth floor.

How many additional elevators should this building have (assume all elevators begin on the fiftieth floor)?  Provide a quantifiable justification to support your answer (e.g. defend why 2 elevators are better than any other case, or 3, or 4 or...so on.)

Edited by BMAD, 25 March 2014 - 02:43 PM.

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### #2 k-man

k-man

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Posted 25 March 2014 - 06:52 PM

Can you clarify these points?

1) If there are 2 elevators starting from 50th floor, will 2 people get on the same elevator? 1 on each? Do we have freedom to choose how to distribute people to elevators?

2) If there are 2 or more elevators will they all stop on the 49th floor? Or only one will stop and the others will skip it?  If latter, can we choose which elevator will stop on what floor?

3) If the elevator reaches capacity and the floor below doesn't have anyone waiting, will it travel to the next floor that has people waiting? Or will it unload on the next floor below and continue empty?

4) What's the optimization criteria? Are we looking for the minimum number of elevators required to get these people where they want to go in the shortest time possible?

Thanks

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Posted 25 March 2014 - 07:48 PM

1. Assume that all people get in the same elevator until that elevator hits capacity. So with two elevators, the first opens on the 50th while the next skips and goes to the 49th. They would keep doing this alternating pattern until or unless the lower elevator hits capacity and goes down only one floor.

2. I think this question is answered above.

3.the elevator can only go one additional floor once it reaches capacity.

4. Optimation: think of your own algorithm that achieves this..... the amount of elevators needed to allow for the quickest "movement" of users to their destination while penalizing your solution based on your elevator selection....think of it as diminishing returns
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