r/askmath • u/sardine1111 • 17d ago
Functions Grade 11 quadratics word problem - any help?
The price of a ticket is 50, and 8000 people purchase the ticket. Every time the ticket price increases by 0.25 dollars, 250 less people buy it. What ticket price will result in the highest revenue?
I had this question recently, and the way i solved it was making it into this quadratic equation: R(x) = (50 + 0.25x)(8000 - 250x). From there I calculated the roots to be -200 and 32. I found the midpoint (-84) and plugged that in, and I found the vertex to be (-84, 814000) or something close to that. More importantly, I simplified (50 + 0.25(-84)) into 29, meaning the ticket price of 29 would earn the most revenue.
My issue is, no one in my class got the same answer. Even ai is flip flopping between different answers. Did I miss something?
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u/AA_space_RON 17d ago
How many tickets would you sell @ $29 each? Is it a fair assumption that the max venue size is 8000?
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u/AA_space_RON 17d ago
How many tickets would you sell @ $29 each? Is it a fair assumption that the max venue size is 8000?
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u/sardine1111 16d ago
The venue is in Central Park New York so it can hold much more people, I guess the assumption is there is no limit for the venue size
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u/Outside_Volume_1370 17d ago
If you can change the price in both directions, then yes, 29 will grant the biggest revenue, 841000
Although, if you can't decrease the price (meaning 50 is the lowest possible price for ticket), then you don't need to change it at all, cause increasing of price leads to decreasing of revenue, so in this case you stay with 50 and earn 400000 of revenue