Question

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?

Answer 1

i can help...maybe

Answer 2

you doing this for calculus right?

Answer 3

mixed math grade 11

Answer 4

do you know what a "derivative" is yet?

Answer 5

not yet, no

Answer 6

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

Answer 7

sure *!

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

alright

Answer 12

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?

Answer 13

okay i understand that

Answer 14

a = first = -25; b = middle = 100

Do you agree with this?

Answer 15

yes

Answer 16

-b/2a:

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

Answer 17

wait, where did u get the 2?

Answer 18

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

Answer 19

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

Answer 20

how does the quadratic formula go again?

Answer 21

Its got two parts to it; or rather, we can seperate it into 2 parts like this:

-b/2a +- sqrt(b^2-4ac)/2a

Answer 22

what is the slash?

Answer 23

1/2 means 1 divided by 2 .... which means one-half.....

but for now, just see it as a fraction bar

Answer 24

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

Answer 25

-b (+-) sqrt(b^2-4ac)
--- ------------
2a 2a

Does this help?

Answer 26

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

Answer 27

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

Answer 28

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?

Answer 29

yes

Answer 30

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?

Answer 31

yes i think so

Answer 32

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?

Answer 33

yes i agree

Answer 34

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?

Answer 35

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

Answer 36

lol..... youre welcome :)