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Math Help - modeling with functions

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    Exclamation modeling with functions

    I need help with this exercise. I don't know how to make the equation for the function ergo I don't know how the function

    a rancher with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle

    a) find a function that models the total area of the four pens
    b) find the largest possible total area of the four pens
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    Quote Originally Posted by cristinaivelisse View Post
    I need help with this exercise. I don't know how to make the equation for the function ergo I don't know how the function

    a rancher with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle

    a) find a function that models the total area of the four pens
    b) find the largest possible total area of the four pens
    1. Draw a sketch.

    2. The complete area is calculated by: A = l \cdot w

    3. The fencing consists of 2 lengthes and 5 width:

    2l+5w=750~\implies~w=150-\frac25 l

    4. Plug in this term into the equation of the area to get the equation of the function:

    A(l)=l\cdot \left(150-\frac25 l \right) = 150 l - \frac25 l^2

    5. The graph of the function is a parabola opening down with it's maximum value at it's vertex. Determine the coordinates of the vertex to get the value of l when the largest area occurs.
    Spoiler:
    I've got l = 187.5' and w = 75'
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