An auditorium has seats for $3,200$ people. Tickets to attend a show …

Question

Prompt

An auditorium has seats for

3, 200

people. Tickets to attend a show at the auditorium currently cost

\

8.00

. F or e a c h

$1.00

in cr e a se t o t h e t i c k e tp r i ce,

100

f e w er t i c k e t s w i l l b eso l d . T hi ss i t u a t i o n c anb e m o d e l e d b y t h ee q u a t i o n

y = -100x^2 + 2,400x + 25,600

, w h er e

r e p r ese n t s t h e in cr e a se in t i c k e tp r i ce, in d o l l a r s, an d

r e p r ese n t s t h er e v e n u e, in d o l l a r s, f r o m t i c k e t s a l es . I f t hi se q u a t i o ni s g r a p h e d in t h e

- pl an e, a tw ha t v a l u eo f

x$ is the maximum of the graph?