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mathcalculus

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.)

  • 5 months ago
  • 5 months ago

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  1. mathcalculus
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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?

    • 5 months ago
  2. mathcalculus
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    @agent0smith

    • 5 months ago
  3. mathcalculus
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    @pgpilot326

    • 5 months ago
  4. mathcalculus
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    @zepdrix

    • 5 months ago
  5. mathcalculus
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    17/2*

    • 5 months ago
  6. pgpilot326
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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.

    • 5 months ago
  7. mathcalculus
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    yes i did it exactly like that

    • 5 months ago
  8. pgpilot326
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    and the max occured at 17/2?

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

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

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

    • 5 months ago
  12. mathcalculus
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    i set that to zero and got 17/2

    • 5 months ago
  13. pgpilot326
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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 $

    • 5 months ago
  14. pgpilot326
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    by yield, i mean total yield, not yield per tree.

    • 5 months ago
  15. pgpilot326
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    x = 8 => 2655 peaches x = 9 => 2655 peaches

    • 5 months ago
  16. mathcalculus
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    i tried those also

    • 5 months ago
  17. mathcalculus
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    it says wrong

    • 5 months ago
  18. mathcalculus
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    • 5 months ago
  19. pgpilot326
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    did you try 8?

    • 5 months ago
  20. mathcalculus
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    yeah

    • 5 months ago
  21. mathcalculus
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    :/

    • 5 months ago
  22. pgpilot326
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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)?

    • 5 months ago
  23. mathcalculus
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    woahhhh how is it 59?

    • 5 months ago
  24. mathcalculus
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    its saying correct to that one

    • 5 months ago
  25. mathcalculus
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    did you use the second derivative test? or something?

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

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

    • 5 months ago
  28. mathcalculus
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    so wouldnt it be 60?

    • 5 months ago
  29. pgpilot326
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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.

    • 5 months ago
  30. mathcalculus
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    ok...

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

    • 5 months ago
  32. mathcalculus
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    im a little confused on that.

    • 5 months ago
  33. mathcalculus
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    yeah i tried 60 but it kept saying wrong.

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

    • 5 months ago
  35. mathcalculus
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    meaning 51+ 9....

    • 5 months ago
  36. pgpilot326
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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?

    • 5 months ago
  37. mathcalculus
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    huh?

    • 5 months ago
  38. pgpilot326
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    how old are you?

    • 5 months ago
  39. mathcalculus
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    this example sounds scary.

    • 5 months ago
  40. pgpilot326
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    yeah, intentionally.

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

    • 5 months ago
  42. mathcalculus
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    thanks anyways, i see the problem clearly now.

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

    • 5 months ago
  44. mathcalculus
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    thanks again!

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

    • 5 months ago
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