) 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?

Question

) 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?

jack1 · Answer

$\large R = 8000 + 760x - 30x^2$
maximum occurs at the turning point of this line
can you work out the turning point of a parabola?

anonymous · Answer

i tried using the -b/2(a) and then plugging that result for x but thats where i get lost

jack1 · Answer

have you worked with derivatives yet?

anonymous · Answer

no.

jack1 · Answer

damn... k hang on

jack1 · Answer

For $\Large y = ax^2 + bx + c$
$\Large (c - \frac{b^2}{4a}) = ymax~~ or~~ ymin$ value at the max point

jack1 · Answer

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 · Answer

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 · Answer

the answer i got was 11400

anonymous · Answer

these were the options 
A) $9,920 B) $13,530 C) $12,813 D) no maximum

jack1 · Answer

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 · Answer

yes, i have just never used that formula before that's why. thank you :)

jack1 · Answer

welcomes ;)