<PRE><B>Question 337535</B>
Revenue = f ( Ticket Price, Tickets Sold ) = Price*Sold 

Tickets Sold = f ( Price ) = m*Price + b
Sold = -10/(0.2)*(Price) +b 
500 = -10/(0.2)*(8) + b
900 = b
Ticket Sold = -10/(0.2)*Price + 900
Tickets Sold = -50*Price + 900

Revenue = Price * Sold = Price * (-50*Price + 900)
Revenue = -50*Price^2 + 900*Price

Take the derivative and set to 0:
dRev = -100*Price + 900
0 = -100*Price+900
Price = 9.00

This is a maximum because the second derivative is negative:
d^2Rev = -100
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