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'- subject to availability -' (Posted on 2022-06-02) Difficulty: 3 of 5

A passenger aircraft seats 210 passengers in economy class, 7 abreast in rows 30 to 59. All seats are full for the current trip.

The in-flight menu for economy passengers has 3 main-course choices: curried mutton with rice, chicken supreme with brocolli, and pork belly with bean sprouts. Given that, on average, one-third of the passengers will prefer each main-course choice, the aircraft carries 70 meals of each type.

The meals are served from large trolleys that the servers push through the aircraft from row 30 abaft. Each passenger in turn is asked which meal they choose. Naturally, this depends on individual preference, but overall each choice is equally likely. Subject to availability, the passenger is then handed their selection.

Questions:
(1) In what row will at least one main-course choice likely become unavailable?
(2) How many passengers will likely receive a non-preferred meal?

No Solution Yet Submitted by broll    
Rating: 2.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
We need a third simulation | Comment 3 of 7 |
If a passengers' first choice is unavailable, Charlie has simulated two different strategies for picking what he does get:
a) Randomly picking a substitute or
b) Predetermining the order in which meals will be used as a substitute.

But neither is optimal in terms of maximizing the number of passengers who receive their preferred meal.  The optimal strategy has been mentioned by Steven Lord:
c) Use as a substitute whichever meal constitutes the most remaining.

  Posted by Steve Herman on 2022-06-02 12:36:35
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