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In a movie theatre two movies 'Avengers' and 'Inception' with running time of 3 & 4 hours respectively and ticket price of 15$ & 25$ respectively will be shown. Within 24 hours they will be shown for a & b times respectively such that a,b >= 1. What will be the value of a+b so that the theatre owner make the maximum profit out of it? My confusion: Here is it necessay to keep the theatre running for all 24 hours or it can be closed before 24 hours if the owner can make maximum profit??

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IMO,
"a"(shows of Avengers (15$/show)) must be 1 and "b"(shows of Inception(25$/show)) must be 5.i.e.
1 * 3 hrs = 3 hrs per day for Avengers, where as
5 * 4 hrs = 20 hrs per day for Inception
hence total running hrs will be 3 + 20 = 23,
Total Daily collection = (15*1) + (25*5) = 140$

So answer to your question is 6 shows per day so that the theatre owner make the maximum profit.

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  • Yes I've got the similar answer so it is not a problem if we close before 24 hours right? Jan 22, 2020 at 12:45

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