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mathcalculus

  • one year ago

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.)

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  1. mathcalculus
    • one year ago
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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?

  2. mathcalculus
    • one year ago
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    @agent0smith

  3. mathcalculus
    • one year ago
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    @pgpilot326

  4. mathcalculus
    • one year ago
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    @zepdrix

  5. mathcalculus
    • one year ago
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    17/2*

  6. pgpilot326
    • one year ago
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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.

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

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

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

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

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

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

  13. pgpilot326
    • one year ago
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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 $

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

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

  16. mathcalculus
    • one year ago
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    i tried those also

  17. mathcalculus
    • one year ago
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    it says wrong

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

  20. mathcalculus
    • one year ago
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    yeah

  21. mathcalculus
    • one year ago
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    :/

  22. pgpilot326
    • one year ago
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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)?

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

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

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

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

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

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

  29. pgpilot326
    • one year ago
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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.

  30. mathcalculus
    • one year ago
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    ok...

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

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

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

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

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

  36. pgpilot326
    • one year ago
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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?

  37. mathcalculus
    • one year ago
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    huh?

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

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

  40. pgpilot326
    • one year ago
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    yeah, intentionally.

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

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

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

  44. mathcalculus
    • one year ago
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    thanks again!

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

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