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Question 229242: Hello. I'm working on a question in Algebra 2 in quadratics. It says:
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 figured out that charging $2 and $4 was the same profit ($400 a day), so that means the answer is $3, but I need to show my work in a h(t)=-.5gt+vt+h, where V and H are sub 0. How does this problem fit into that formula?
Found 2 solutions by ankor@dixie-net.com, cornball3440:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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
Answer by cornball3440(16)  (Show Source):
You can put this solution on YOUR website! 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 figured out that charging $2 and $4 was the same profit ($400 a day), so that means the answer is $3, but I need to show my work in a h(t)=-.5gt+vt+h, where V and H are sub 0. How does this problem fit into that formula?
---
If your teacher requires work in that formula, then so be it.
Your gravity is one day, your velocity is 10t (Explained later), and the original one day total is 400. The 400 is found by multiplying $2 by 200 cassettes, and since your One Day decreases by 5 customers a day, it's found by the -1/2 multiplied by the H sub Zero, 10. So the H was found by dividing 5 and a Positive (Opposite) 1/2.
In thus, it's symmetrical t point for the function of t is 10. (-b/2a or -10/[2(-1/2)])
The Increments were in $.1, so 10($.1)=$1
The Original $2 added to this new $1 is your answer of $3, which you got.
And if you need to also know how much money that is, plug it into the original idea, which is simpler. 10*5=50, so 200-50 is 150, and 150 customers buying at $3 a movie is $450 a day for maximum output.
That's quite the brain teaser, I hope you don't have many more like it where work is necessary, or the answer isn't easy to find guess and check tonight or else you'll be up all night.
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