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taranicolee

  • 3 years ago

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

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  1. zordoloom
    • 3 years ago
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    You still there? Do you need help?

  2. taranicolee
    • 3 years ago
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    yes please!

  3. zordoloom
    • 3 years ago
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    Do you know calculus?

  4. taranicolee
    • 3 years ago
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    well haha i'm in the class right now but not really...

  5. zordoloom
    • 3 years ago
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    Okay. That's fine.

  6. taranicolee
    • 3 years ago
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    well are you going to help?(:

  7. zordoloom
    • 3 years ago
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    Do you want just the answer, or how to get the answer?

  8. taranicolee
    • 3 years ago
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    how to get it please (:

  9. taranicolee
    • 3 years ago
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    how to get it please (:

  10. zordoloom
    • 3 years ago
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    okay.

  11. zordoloom
    • 3 years ago
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    let x= the first number let y= the second number

  12. zordoloom
    • 3 years ago
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    so, x+2y=100.

  13. zordoloom
    • 3 years ago
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    You are trying to maximize the product yz. so let z= the product = to xy

  14. zordoloom
    • 3 years ago
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    Following so far?

  15. taranicolee
    • 3 years ago
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    yeah(:

  16. zordoloom
    • 3 years ago
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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

  17. zordoloom
    • 3 years ago
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    Now, just find the vertex of that graph using -b/2a

  18. zordoloom
    • 3 years ago
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    Therefore, the first value is 25 and the second value is 50.

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

  20. zordoloom
    • 3 years ago
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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.

  21. zordoloom
    • 3 years ago
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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)

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

  23. zordoloom
    • 3 years ago
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    P = xy = (100 − 2y)y = 100y − 2y^2

  24. zordoloom
    • 3 years ago
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    Sure.

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