A home gardener estimates that 24 apple trees will have an average yield of 104 apples per tree. But because of the size of the garden, for

Question

A home gardener estimates that 24 apple trees will have an average yield of 104 apples per tree. But because of the size of the garden, for each additional tree planted the yield will decrease by two apples per tree. (a) How many additional trees should be planted to maximize the total yield of apples

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Khải Quang 5 months 2021-08-09T00:11:30+00:00 1 Answers 41 views 0

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    2021-08-09T00:12:50+00:00

    Answer:

    The farmer should plant 14 additional trees, for maximum yield.

    Step-by-step explanation:

    Given

    Trees = 24

    Yield = 104

    x \to additional\ trees

    So, we have:

    Trees = 24 + x

    Yield = 104 - 2x

    Required

    The additional trees to be planted for maximum yield

    The function is:

    f(x) = Trees * Yield

    f(x) = (24 + x) * (104 - 2x)

    Open bracket

    f(x) = 24 * 104 + 104x - 24 * 2x - x * 2x

    f(x) = 2796 + 104x - 48x - 2x^2

    f(x) = 2796 + 56x - 2x^2

    Rewrite as:

    f(x) = - 2x^2 + 56x + 2796

    Differentiate

    f'(x) = -4x + 56

    Equate f'(x) = -4x + 56 to 0 and solve for x to get the maximum of x

    -4x + 56 = 0

    -4x =- 56

    Divide by -4

    x =14

    The farmer should plant 14 additional trees, for maximum yield.

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )