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brendakayyy

  • 2 years ago

help me with optimization for calculus

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  1. brendakayyy
    • 2 years ago
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    a computer company determines its profit equation in millions of dollars given by p=x^3-48x^2+720x-1000 where x is the number of thousands of units of software sold

  2. brendakayyy
    • 2 years ago
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    and 0<x<40 optimize the manufactures profit

  3. Goten77
    • 2 years ago
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    im thinking this is really ez.... but maybe im wrong.... since from 0-40 it looks like a line almost.... wouldnt (40,y) b the maximum?

  4. Goten77
    • 2 years ago
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    or maybe im wrong

  5. zepdrix
    • 2 years ago
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    |dw:1355889094401:dw|It's a cubic function, so it's going to have this shape. As I've illustrated in the picture, it is possible that 40 might not be the maximum profit value. So we'll have to do some work to find out where that point is.

  6. brendakayyy
    • 2 years ago
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    do i differentiate the function and find the critical values?

  7. zepdrix
    • 2 years ago
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    \[\large P(x)=x^3-48x^2+720x-1000\]Yes very good. You'll want to find Critical Points, and since this is a CLOSED INTERVAL, also check the END POINTS! Then simply plug each value into the function, and see which gives you the largest output.

  8. Goten77
    • 2 years ago
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    oh if thats how it looked then i graphed it wrong.. my bad

  9. zepdrix
    • 2 years ago
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    Hmm I better throw it into wolfram and make sure I'm not way off.. cause I was just doing that based off of memory :P

  10. Goten77
    • 2 years ago
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    but anyways it be best to just find derivative.. and critical points.. then find values of those and the 0/40 and then u get ur answer

  11. brendakayyy
    • 2 years ago
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    would my critical values be x<12, 12<x<20, X>20?

  12. Goten77
    • 2 years ago
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    ur critical valued would be points.....

  13. Goten77
    • 2 years ago
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    |dw:1355889480030:dw|

  14. zepdrix
    • 2 years ago
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    You got the correct points, x=12, x=20. I'm not sure why you wrote them as intervals though :)

  15. Goten77
    • 2 years ago
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    ^ye

  16. zepdrix
    • 2 years ago
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    Now you want to plug your values into P(x) and compare, to find out which one gives you the largest value within this closed interval.\[\large P(12),\quad P(20), \quad P(0), \quad P(40)\]

  17. brendakayyy
    • 2 years ago
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    well cuz you base your values off the intervals according to my teacher

  18. brendakayyy
    • 2 years ago
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    what equation would i plug that into?

  19. zepdrix
    • 2 years ago
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    The original equation.

  20. brendakayyy
    • 2 years ago
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    ok got it

  21. brendakayyy
    • 2 years ago
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    whered you get the P(40) and P(0)

  22. Goten77
    • 2 years ago
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    there apart of the domain.. so there possible maxs's mins

  23. brendakayyy
    • 2 years ago
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    oh thats what was meant by end points so if it were aclosed interval i would not take the end points into consideration right?

  24. brendakayyy
    • 2 years ago
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    what are the dimensions of the square based open top box that has a volume of 20 cubic inches and smallest surface area?

  25. brendakayyy
    • 2 years ago
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    can someone help me with this one ^

  26. Zarkon
    • 2 years ago
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    if you have a new question you should put it in a new thread

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