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. What is the largest income? 
let x=number of £0.50 increases
I(x)=price*people attending
=(0.50+ 0.05x)(10000-200x)
=5000+500x-100x-10x^2
=-10x^2+400x+5000=0
=-x^2+40x+500=0
complete the square:
=-(x^2-40+400)+400+500
=-(x-20)^2+900
This is an equation of a parabola that opens down with vertex at (20,900)
maximum income occurs when x=20 or 20*£0.05=£0.10, which results in an admission price of £0.60
admission price that yields the largest income=£0.60
What is the largest income? £900