Question 564173
A school concert usually attracts 600 people at a cost of $10 per person.
 On average for every $1 rise in admission price, 50 less people attend the concert.
 If T is the total amount of takings and n is the number of $1 increases write a rule for the function which gives T in terms of n. 
The equation:
Total = no. of people * cost for each ticket
Which is
T(n) = (600-50n)*(10+n)
FOIL
T(n) = 6000 + 600n - 500n - 50n^2
The quadratic equation which has max value for some value of n
T(n) = -50n^2 + 100n + 6000
:
The parabola will look like this
{{{ graph( 300, 200, -6, 15, -1000, 7000, -50x^2+100x+6000) }}}
Looks like max revenue will occur when n=1, 550 people and $11 ticket $6050