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brendakayyy Group Title

help me with optimization for calculus

  • one year ago
  • one year ago

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  1. brendakayyy Group Title
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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

    • one year ago
  2. brendakayyy Group Title
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    and 0<x<40 optimize the manufactures profit

    • one year ago
  3. Goten77 Group Title
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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?

    • one year ago
  4. Goten77 Group Title
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    or maybe im wrong

    • one year ago
  5. zepdrix Group Title
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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.

    • one year ago
  6. brendakayyy Group Title
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    do i differentiate the function and find the critical values?

    • one year ago
  7. zepdrix Group Title
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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.

    • one year ago
  8. Goten77 Group Title
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    oh if thats how it looked then i graphed it wrong.. my bad

    • one year ago
  9. zepdrix Group Title
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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

    • one year ago
  10. Goten77 Group Title
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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

    • one year ago
  11. brendakayyy Group Title
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    would my critical values be x<12, 12<x<20, X>20?

    • one year ago
  12. Goten77 Group Title
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    ur critical valued would be points.....

    • one year ago
  13. Goten77 Group Title
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    |dw:1355889480030:dw|

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

    • one year ago
  15. Goten77 Group Title
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    ^ye

    • one year ago
  16. zepdrix Group Title
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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.\[\large P(12),\quad P(20), \quad P(0), \quad P(40)\]

    • one year ago
  17. brendakayyy Group Title
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    well cuz you base your values off the intervals according to my teacher

    • one year ago
  18. brendakayyy Group Title
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    what equation would i plug that into?

    • one year ago
  19. zepdrix Group Title
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    The original equation.

    • one year ago
  20. brendakayyy Group Title
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    ok got it

    • one year ago
  21. brendakayyy Group Title
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    whered you get the P(40) and P(0)

    • one year ago
  22. Goten77 Group Title
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    there apart of the domain.. so there possible maxs's mins

    • one year ago
  23. brendakayyy Group Title
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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?

    • one year ago
  24. brendakayyy Group Title
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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?

    • one year ago
  25. brendakayyy Group Title
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    can someone help me with this one ^

    • one year ago
  26. Zarkon Group Title
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    if you have a new question you should put it in a new thread

    • one year ago
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