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taranicolee Group Title

can someone explain to me how to find two positive numbers such that the sum of the first and twice the second is 100 and their product is a maximum

  • one year ago
  • one year ago

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  1. zordoloom Group Title
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    You still there? Do you need help?

    • one year ago
  2. taranicolee Group Title
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    yes please!

    • one year ago
  3. zordoloom Group Title
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    Do you know calculus?

    • one year ago
  4. taranicolee Group Title
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    well haha i'm in the class right now but not really...

    • one year ago
  5. zordoloom Group Title
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    Okay. That's fine.

    • one year ago
  6. taranicolee Group Title
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    well are you going to help?(:

    • one year ago
  7. zordoloom Group Title
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    Do you want just the answer, or how to get the answer?

    • one year ago
  8. taranicolee Group Title
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    how to get it please (:

    • one year ago
  9. taranicolee Group Title
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    how to get it please (:

    • one year ago
  10. zordoloom Group Title
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    okay.

    • one year ago
  11. zordoloom Group Title
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    let x= the first number let y= the second number

    • one year ago
  12. zordoloom Group Title
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    so, x+2y=100.

    • one year ago
  13. zordoloom Group Title
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    You are trying to maximize the product yz. so let z= the product = to xy

    • one year ago
  14. zordoloom Group Title
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    Following so far?

    • one year ago
  15. taranicolee Group Title
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    yeah(:

    • one year ago
  16. zordoloom Group Title
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    okay, so solve x+2y=100 for x. x=100-2y z=xy z=(100-2y)y z=y(100-2y) z=100y-2y^2

    • one year ago
  17. zordoloom Group Title
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    Now, just find the vertex of that graph using -b/2a

    • one year ago
  18. zordoloom Group Title
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    Therefore, the first value is 25 and the second value is 50.

    • one year ago
  19. zordoloom Group Title
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    Let me simplify this down a bit, because I was writing out my work which may be a bit confusing.

    • one year ago
  20. zordoloom Group Title
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    So, you have been told that the sum of the first number, twice the second is 100 (I'll use just x and y this time to make things less confusing) so, x+2y=100.

    • one year ago
  21. zordoloom Group Title
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    You are trying to minimize the product, P=xy. So solve the first equation x+2y=100, for x.........x=100-2y. Now substitute this into the product formula ( P=xy)

    • one year ago
  22. taranicolee Group Title
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    ohhh wait i get it! thank you!!!! do you have time to help me with another one?(:

    • one year ago
  23. zordoloom Group Title
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    P = xy = (100 − 2y)y = 100y − 2y^2

    • one year ago
  24. zordoloom Group Title
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    Sure.

    • one year ago
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