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mathcalculus Group Title

An orchard contains 51 peach trees with each tree yielding an average of 51 peaches. For each 4 additional trees planted, the average yield per tree decreases by 3 peaches. How many trees should be planted to maximize the total yield of the orchard? The number of trees is . (Give your answer as a whole number.)

  • one year ago
  • one year ago

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  1. mathcalculus Group Title
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    I got my answer 17/.. but they want it as a whole number. any ideas what i might have done wrong?

    • one year ago
  2. mathcalculus Group Title
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    @agent0smith

    • one year ago
  3. mathcalculus Group Title
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    @pgpilot326

    • one year ago
  4. mathcalculus Group Title
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    @zepdrix

    • one year ago
  5. mathcalculus Group Title
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    17/2*

    • one year ago
  6. pgpilot326 Group Title
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    total peaches = (51 - (3/4) x)*(51+x) where x = # number of additional trees. maximize and if it's not an integer, which ever integer is closest will do the job.

    • one year ago
  7. mathcalculus Group Title
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    yes i did it exactly like that

    • one year ago
  8. pgpilot326 Group Title
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    and the max occured at 17/2?

    • one year ago
  9. mathcalculus Group Title
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    then i multiplied them out and to maximize I found the derivative.

    • one year ago
  10. mathcalculus Group Title
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    well i got f(x)= -3x^2/4+51x/4+2601

    • one year ago
  11. mathcalculus Group Title
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    and f '(x)= -6x/4+51/4

    • one year ago
  12. mathcalculus Group Title
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    i set that to zero and got 17/2

    • one year ago
  13. pgpilot326 Group Title
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    so check the yield at x = 8 and x = 9. they're likely the same so either would work. but if you're a farmer, you go with less additional trees to save $

    • one year ago
  14. pgpilot326 Group Title
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    by yield, i mean total yield, not yield per tree.

    • one year ago
  15. pgpilot326 Group Title
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    x = 8 => 2655 peaches x = 9 => 2655 peaches

    • one year ago
  16. mathcalculus Group Title
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    i tried those also

    • one year ago
  17. mathcalculus Group Title
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    it says wrong

    • one year ago
  18. mathcalculus Group Title
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    • one year ago
  19. pgpilot326 Group Title
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    did you try 8?

    • one year ago
  20. mathcalculus Group Title
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    yeah

    • one year ago
  21. mathcalculus Group Title
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    :/

    • one year ago
  22. pgpilot326 Group Title
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    i don't know what to tell you. could it be they want 59 as the asnwer (total number of trees in the orchard)?

    • one year ago
  23. mathcalculus Group Title
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    woahhhh how is it 59?

    • one year ago
  24. mathcalculus Group Title
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    its saying correct to that one

    • one year ago
  25. mathcalculus Group Title
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    did you use the second derivative test? or something?

    • one year ago
  26. pgpilot326 Group Title
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    51 + 8 = 59. there were 51 already planted plus the 8 you added to maximize the total yield.

    • one year ago
  27. mathcalculus Group Title
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    but if it's 8.5 shouldnt we round it to 9?

    • one year ago
  28. mathcalculus Group Title
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    so wouldnt it be 60?

    • one year ago
  29. pgpilot326 Group Title
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    question wasn't clear... should have said total number of trees planted in the orchard. you have to think like a farmer. one less tree gives the same yield as one more. what would be better? think of not only the initial cost of the tree but also the watering and care, etc.

    • one year ago
  30. mathcalculus Group Title
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    ok...

    • one year ago
  31. pgpilot326 Group Title
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    maybe 60 would also work (as an answer) but it's not as practical as 59.

    • one year ago
  32. mathcalculus Group Title
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    im a little confused on that.

    • one year ago
  33. mathcalculus Group Title
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    yeah i tried 60 but it kept saying wrong.

    • one year ago
  34. mathcalculus Group Title
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    i mean mathematically speaking best round is 60 and then adding it to the already planted trees

    • one year ago
  35. mathcalculus Group Title
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    meaning 51+ 9....

    • one year ago
  36. pgpilot326 Group Title
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    again, you have think like a business person/farmer. think of the problem like this: if you had to cut off fingers to get gold coins in the same scenario, you'd want to cut off as few fingers as possible in order to maximize the number of gold coins. if you got the same number of gold coins for cutting of 8 fingers as you would for cutting off 9 fingers, how many fingers would you cut off?

    • one year ago
  37. mathcalculus Group Title
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    huh?

    • one year ago
  38. pgpilot326 Group Title
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    how old are you?

    • one year ago
  39. mathcalculus Group Title
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    this example sounds scary.

    • one year ago
  40. pgpilot326 Group Title
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    yeah, intentionally.

    • one year ago
  41. mathcalculus Group Title
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    i understand you, but i just don't like the example.lol

    • one year ago
  42. mathcalculus Group Title
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    thanks anyways, i see the problem clearly now.

    • one year ago
  43. pgpilot326 Group Title
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    lol, sorry. it's just what popped out of my head.

    • one year ago
  44. mathcalculus Group Title
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    thanks again!

    • one year ago
  45. pgpilot326 Group Title
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    excellent. ask your teacher to be more explicit in what is wanted next time. you're welcome!

    • one year ago
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