anonymous
  • anonymous
) A hotel finds that its revenue is given by R = 8000 + 760x - 30x2 when it charges 80 + 10x dollars for a room. To the nearest dollar, what is the maximum revenue it can earn?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Jack1
  • Jack1
\(\large R = 8000 + 760x - 30x^2\) maximum occurs at the turning point of this line can you work out the turning point of a parabola?
anonymous
  • anonymous
i tried using the -b/2(a) and then plugging that result for x but thats where i get lost
Jack1
  • Jack1
have you worked with derivatives yet?

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anonymous
  • anonymous
no.
Jack1
  • Jack1
damn... k hang on
Jack1
  • Jack1
For \(\Large y = ax^2 + bx + c\) \(\Large (c - \frac{b^2}{4a}) = ymax~~ or~~ ymin\) value at the max point
Jack1
  • Jack1
so ur equation is \(\large R = 8000 + 760x - 30x^2\) \(\large y = ax^2 + bx + c\) so a = -30 b = 760 c = 8000 no can you solve for ymax?
anonymous
  • anonymous
this was the answer in the help video but i think it's wrong. R=(80+10x)(100-3x) 8000-24x+1000x-30x^2 R=-30x^2+976+8000 X= -b/2a= -976/2(-30) and with all of that i was suppposed to end up with $12813 for the maximum
anonymous
  • anonymous
the answer i got was 11400
anonymous
  • anonymous
these were the options A) $9,920 B) $13,530 C) $12,813 D) no maximum
Jack1
  • Jack1
hmm... 12813 is correct using ymax = c - (b^2)/4a ymax = 8000 - 760^2/4(-30) ymax = 8000 - 57760/-120 ymax = 8000 + 4813.33 = $12813 ... does this kinda make ssense tho?
anonymous
  • anonymous
yes, i have just never used that formula before that's why. thank you :)
Jack1
  • Jack1
welcomes ;)

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