Question 887660
When the admission price to a game is £0.50, 10,000 people attend.
 For every increase of £0.05 in the admission price, 200 fewer people attend.
 Find the admission price that yields the largest income. 
:
let x = no. of 5 cent increases, also = the multiple of 200 people decreases
:
Income = price * no. of people
I = (.50+.05x)(10000-200x)
FOIL
I = 5000 - 100x + 500x - 10x^2
Combine to form a quadratic equation
I = -10x^2 + 400x + 5000
simplify divide by 10
I = -x^2 + 40x + 500
The min will occur at the axis of symmetry, x = -b(2a)
x = {{{(-40)/(2*-1)}}}
x = 20 five cent increases
therefore
1.50 is the increased price
and
10000 -(20*200) = 6000 people
"What is the largest income? "
$1.50 * 6000 = $9000 is the max income