can anyone help me with this? Heres the question: The student council is selling cases of gift cards as a fundraiser. The revenue, r(x), in dollars, can be modelled by the function R(x)= -25x(squared) +100x +1500, where x is the number of cases of gift cards sold. How many cases must be sold to maximize the revenue?

- anonymous

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- amistre64

i can help...maybe

- amistre64

you doing this for calculus right?

- anonymous

mixed math grade 11

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- amistre64

do you know what a "derivative" is yet?

- anonymous

not yet, no

- amistre64

Its alot quicker with the "derivative"; but we can do it without... you up for it?

- anonymous

sure *!

- amistre64

have you gone over the quadratic equation or "completeing the square" yet?

- anonymous

yes, but i do not remember how to complete the square unfortunately

- amistre64

thats ok, completing the square is PROOF that the quadratic formula works...

- anonymous

alright

- amistre64

the only thing we are concerned about with the quadratic formula is what we get for -b/(2a) cause that gives us the x value for where this equation bends over itself. It looks like aupside down bowl. Ok?

- anonymous

okay i understand that

- amistre64

a = first = -25; b = middle = 100
Do you agree with this?

- anonymous

yes

- amistre64

-b/2a:
-(100)/(2(-25)) = -50/-25 = -2/-1 = 2. Am I right?

- anonymous

wait, where did u get the 2?

- amistre64

Im old now, so I could be forgetting something :)

- amistre64

which one? the -b/2a..that 2?

- anonymous

how does the quadratic formula go again?

- amistre64

Its got two parts to it; or rather, we can seperate it into 2 parts like this:
-b/2a +- sqrt(b^2-4ac)/2a

- anonymous

what is the slash?

- amistre64

1/2 means 1 divided by 2 .... which means one-half.....
but for now, just see it as a fraction bar

- anonymous

alright, i think i understand now. so just substitute the numbers into the quadratic formula and i shall get 2? that is the answer in the back of the book

- amistre64

-b (+-) sqrt(b^2-4ac)
--- ------------
2a 2a
Does this help?

- amistre64

Yes, but the only thing we care about for finding the maximum amount is what happens at x = -b/2a

- anonymous

so basically just use x= -b divided by 2a and i will get the answer of 2?

- amistre64

Lets find out, cause I could have messed it up in my head :)
-100 divided by 2(-25) = what?
-100 divided by -50 = 2 right?

- anonymous

yes

- amistre64

Now that we now the value of "x" that will give us the most stuff, lets plug it into the original equation to figure out HOW MUCH stuff we get..... you agree?

- anonymous

yes i think so

- amistre64

R(x)= -25(2)^2 +100(2) +1500
R(x)= -25(4) + 200 + 1500
R(x)= -100 + 200 + 1500
R(x) = 100 +1500
R(x) = 1600
Do you agree?

- anonymous

yes i agree

- amistre64

the derivative of:
R(x)= -25x^2 +100x +1500
is -50x +100. And when the derivative = 0 we get the max amount:
when x=100/50 = 2 the derivative = 0. Do you see that?

- anonymous

thats kind of confusing... but you helped me find out how to get the right answer it really helped thanks!

- amistre64

lol..... youre welcome :)

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