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anonymous

  • 2 years 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. anonymous
    • 2 years 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. anonymous
    • 2 years ago
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    @agent0smith

  3. anonymous
    • 2 years ago
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    @pgpilot326

  4. anonymous
    • 2 years ago
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    @zepdrix

  5. anonymous
    • 2 years ago
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    17/2*

  6. anonymous
    • 2 years 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. anonymous
    • 2 years ago
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    yes i did it exactly like that

  8. anonymous
    • 2 years ago
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    and the max occured at 17/2?

  9. anonymous
    • 2 years ago
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    then i multiplied them out and to maximize I found the derivative.

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

  11. anonymous
    • 2 years ago
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    and f '(x)= -6x/4+51/4

  12. anonymous
    • 2 years ago
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    i set that to zero and got 17/2

  13. anonymous
    • 2 years 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. anonymous
    • 2 years ago
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    by yield, i mean total yield, not yield per tree.

  15. anonymous
    • 2 years ago
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    x = 8 => 2655 peaches x = 9 => 2655 peaches

  16. anonymous
    • 2 years ago
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    i tried those also

  17. anonymous
    • 2 years ago
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    it says wrong

  18. anonymous
    • 2 years ago
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  19. anonymous
    • 2 years ago
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    did you try 8?

  20. anonymous
    • 2 years ago
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    yeah

  21. anonymous
    • 2 years ago
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    :/

  22. anonymous
    • 2 years 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. anonymous
    • 2 years ago
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    woahhhh how is it 59?

  24. anonymous
    • 2 years ago
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    its saying correct to that one

  25. anonymous
    • 2 years ago
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    did you use the second derivative test? or something?

  26. anonymous
    • 2 years ago
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    51 + 8 = 59. there were 51 already planted plus the 8 you added to maximize the total yield.

  27. anonymous
    • 2 years ago
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    but if it's 8.5 shouldnt we round it to 9?

  28. anonymous
    • 2 years ago
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    so wouldnt it be 60?

  29. anonymous
    • 2 years 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. anonymous
    • 2 years ago
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    ok...

  31. anonymous
    • 2 years ago
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    maybe 60 would also work (as an answer) but it's not as practical as 59.

  32. anonymous
    • 2 years ago
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    im a little confused on that.

  33. anonymous
    • 2 years ago
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    yeah i tried 60 but it kept saying wrong.

  34. anonymous
    • 2 years ago
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    i mean mathematically speaking best round is 60 and then adding it to the already planted trees

  35. anonymous
    • 2 years ago
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    meaning 51+ 9....

  36. anonymous
    • 2 years 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. anonymous
    • 2 years ago
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    huh?

  38. anonymous
    • 2 years ago
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    how old are you?

  39. anonymous
    • 2 years ago
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    this example sounds scary.

  40. anonymous
    • 2 years ago
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    yeah, intentionally.

  41. anonymous
    • 2 years ago
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    i understand you, but i just don't like the example.lol

  42. anonymous
    • 2 years ago
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    thanks anyways, i see the problem clearly now.

  43. anonymous
    • 2 years ago
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    lol, sorry. it's just what popped out of my head.

  44. anonymous
    • 2 years ago
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    thanks again!

  45. anonymous
    • 2 years 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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