Question

Anyone feel like helping out?http://imgur.com/Lzbjezo
I got R(p)=-40p^2+1020p, or R(p)=-40p^2+980 then the maximum would be 12.75, or 12.25...
i feel like 12.75 is correct though.. anyone willing to check my work?

Answer 1

the change in the number of tickets sold divided by the change in price is
\[ \frac{dn}{dp}= \frac{-40}{0.50}= -80 \]
or
dn = -80 dp
now solve
\[ \int dn = -80 \int dp\\
n= -80 p + C
\]
to find C, use the info given:
1000 = -80*8.50+C
C= 1680
thus
n= -80p+1680

the income is price times number of tickets sold: n*p
np= (-80p+1680)p
or
income= -80p^2 +1680p