Question 815773
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
IF 100 seats are sold, the price is $50 per seat.
Each unsold seat increases the price per seat by $1. 
Let x represent the number of unsold seats. 
(a) write an expression for the number of seats sold. (100-x)
(b) Write an expression for the price per seat. {{{(50+ 1(x))}}}
(c) Write an expression for the revenue. R = (100-x)(50+x)
(d) Find the number of unsold seats that will produce the maximum revenue.
    Revenue = 5000 + 50x - x^2  = -(x-25)^2 +625+ 5000 = -(x-25)^2 + 5625
Revenue= -(x-25)^2 + 5625 
Parabola V(25,5625)opening downward
  25 unsold tickets produces the maximum revenue
(e) Find the maximum revenue. $5625
{{{drawing(300,300,   -60, 60, -600, 6000,  blue(line(2,6,2,-6))  , arc(-6,-9,2,-8),grid(1),
circle(25, 5625,2),

graph( 300, 300, -60, 60, -600, 6000,0,-(x-25)^2 + 5625  ))}}}