anonymous
  • anonymous
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?
Mathematics
katieb
  • katieb
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amistre64
  • amistre64
i can help...maybe
amistre64
  • amistre64
you doing this for calculus right?
anonymous
  • anonymous
mixed math grade 11

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amistre64
  • amistre64
do you know what a "derivative" is yet?
anonymous
  • anonymous
not yet, no
amistre64
  • amistre64
Its alot quicker with the "derivative"; but we can do it without... you up for it?
anonymous
  • anonymous
sure *!
amistre64
  • amistre64
have you gone over the quadratic equation or "completeing the square" yet?
anonymous
  • anonymous
yes, but i do not remember how to complete the square unfortunately
amistre64
  • amistre64
thats ok, completing the square is PROOF that the quadratic formula works...
anonymous
  • anonymous
alright
amistre64
  • 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
  • anonymous
okay i understand that
amistre64
  • amistre64
a = first = -25; b = middle = 100 Do you agree with this?
anonymous
  • anonymous
yes
amistre64
  • amistre64
-b/2a: -(100)/(2(-25)) = -50/-25 = -2/-1 = 2. Am I right?
anonymous
  • anonymous
wait, where did u get the 2?
amistre64
  • amistre64
Im old now, so I could be forgetting something :)
amistre64
  • amistre64
which one? the -b/2a..that 2?
anonymous
  • anonymous
how does the quadratic formula go again?
amistre64
  • 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
  • anonymous
what is the slash?
amistre64
  • amistre64
1/2 means 1 divided by 2 .... which means one-half..... but for now, just see it as a fraction bar
anonymous
  • 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
  • amistre64
-b (+-) sqrt(b^2-4ac) --- ------------ 2a 2a Does this help?
amistre64
  • amistre64
Yes, but the only thing we care about for finding the maximum amount is what happens at x = -b/2a
anonymous
  • anonymous
so basically just use x= -b divided by 2a and i will get the answer of 2?
amistre64
  • 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
  • anonymous
yes
amistre64
  • 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
  • anonymous
yes i think so
amistre64
  • 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
  • anonymous
yes i agree
amistre64
  • 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
  • anonymous
thats kind of confusing... but you helped me find out how to get the right answer it really helped thanks!
amistre64
  • amistre64
lol..... youre welcome :)

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