Question 866743
 The owner of a resort offers an organization a 3-day vacation package promo for $5 000 per person if not more than 100 people will take the promo.
 However, he is willing to reduce the cost per person by $25 for every person in excess of 100.
 How many people should take the promo in order for him to receive the largest revenue? 
:
Let x = no. of persons over 100
Let y = total revenue
:
y = (5000-25x)*(100+x)
FOIL
y = 500000 + 5000x - 2500x - 25x^2
A quadratic equation
y = -25x^ + 2500x + 500000
The axis of symmetry, x will give max revenue x = -b/(2a)
x = {{{(-2500)/(2*-25)}}}
x = +50 
we can say 150 people will give max revenue