Question 229242
A store charges $2 for a one-day rental of a video cassette.
 On the average, 200 cassettes are rented from the store each day.
 If a survey indicates that the store's rentals will decrease by and average
 of 5 per day for each 10-cent increase in rental charge, what should the store
 charge to maximize its income?
:
I think you should do it this way
Let x = no. of cassettes less than 200
and
let x = no. of 10 cent increases
:
Let y = income
:
y = (200 - 5x) (2 + .10x)
FOIL
y = 400 + 20x - 10x - .5x^2
:
The quadratic equation
y = -.5x^2 + 10x + 400 
:
Axis of symmetry will give the value for x, for max income x = -b/(2a)
x = -10/(2*-.5)
x = + 10
:
Find max income when x = 10
y = -.5(10^2) + 10(10) + 400
y = -50 + 100 + 400
y = $450 
:
We can say when the price is raised 10(.10) $1, then 200 - 5(10) = 150 will be rented
:
Find the value: 3$ * 150 = $450