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?
Many thanks in advance for your help.
Found 3 solutions by ankor@dixie-net.com, lwsshak3, MathTherapy:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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 = 
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
Answer by lwsshak3(11628)  (Show Source):
You can put this solution on YOUR website! 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
Answer by MathTherapy(10556)  (Show Source):
You can put this solution on YOUR website!
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?
Many thanks in advance for your help.
DUPLICATE
See # 886633
Admission price that yields MAXIMUM income: £
Maximum income: £
You can do the check!!
If you need a complete and detailed solution, let me know!!
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