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anonymous

  • 5 years ago

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?

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  1. amistre64
    • 5 years ago
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    i can help...maybe

  2. amistre64
    • 5 years ago
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    you doing this for calculus right?

  3. anonymous
    • 5 years ago
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    mixed math grade 11

  4. amistre64
    • 5 years ago
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    do you know what a "derivative" is yet?

  5. anonymous
    • 5 years ago
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    not yet, no

  6. amistre64
    • 5 years ago
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    Its alot quicker with the "derivative"; but we can do it without... you up for it?

  7. anonymous
    • 5 years ago
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    sure *!

  8. amistre64
    • 5 years ago
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    have you gone over the quadratic equation or "completeing the square" yet?

  9. anonymous
    • 5 years ago
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    yes, but i do not remember how to complete the square unfortunately

  10. amistre64
    • 5 years ago
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    thats ok, completing the square is PROOF that the quadratic formula works...

  11. anonymous
    • 5 years ago
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    alright

  12. amistre64
    • 5 years ago
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    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?

  13. anonymous
    • 5 years ago
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    okay i understand that

  14. amistre64
    • 5 years ago
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    a = first = -25; b = middle = 100 Do you agree with this?

  15. anonymous
    • 5 years ago
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    yes

  16. amistre64
    • 5 years ago
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    -b/2a: -(100)/(2(-25)) = -50/-25 = -2/-1 = 2. Am I right?

  17. anonymous
    • 5 years ago
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    wait, where did u get the 2?

  18. amistre64
    • 5 years ago
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    Im old now, so I could be forgetting something :)

  19. amistre64
    • 5 years ago
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    which one? the -b/2a..that 2?

  20. anonymous
    • 5 years ago
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    how does the quadratic formula go again?

  21. amistre64
    • 5 years ago
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    Its got two parts to it; or rather, we can seperate it into 2 parts like this: -b/2a +- sqrt(b^2-4ac)/2a

  22. anonymous
    • 5 years ago
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    what is the slash?

  23. amistre64
    • 5 years ago
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    1/2 means 1 divided by 2 .... which means one-half..... but for now, just see it as a fraction bar

  24. anonymous
    • 5 years ago
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    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

  25. amistre64
    • 5 years ago
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    -b (+-) sqrt(b^2-4ac) --- ------------ 2a 2a Does this help?

  26. amistre64
    • 5 years ago
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    Yes, but the only thing we care about for finding the maximum amount is what happens at x = -b/2a

  27. anonymous
    • 5 years ago
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    so basically just use x= -b divided by 2a and i will get the answer of 2?

  28. amistre64
    • 5 years ago
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    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?

  29. anonymous
    • 5 years ago
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    yes

  30. amistre64
    • 5 years ago
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    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?

  31. anonymous
    • 5 years ago
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    yes i think so

  32. amistre64
    • 5 years ago
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    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?

  33. anonymous
    • 5 years ago
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    yes i agree

  34. amistre64
    • 5 years ago
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    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?

  35. anonymous
    • 5 years ago
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    thats kind of confusing... but you helped me find out how to get the right answer it really helped thanks!

  36. amistre64
    • 5 years ago
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    lol..... youre welcome :)

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