You have 600 ft of fencing material to construct a rectangular pen for cattle. What are the dimensions (in feet) of the pen that maximize th

Question

You have 600 ft of fencing material to construct a rectangular pen for cattle. What are the dimensions (in feet) of the pen that maximize the area (enter number only)?

in progress 0
Thiên Di 5 years 2021-07-24T11:54:53+00:00 1 Answers 210 views 0

Answers ( )

  1. ngockhue
    -2
    2021-07-24T11:56:14+00:00
    Reply

    Note that this is still a rectangle, and the length of the fencing is still 600 ft.

                                            o the sum of the sides NOT along the river   x + x + y = 600,  and the area equals xy.

    This makes the two equations:    2x + y = 600,   and A = xy.

    To find the largest area, we need to find A as a function of x or y.  I suggest solving the first equation for y and replacing that in the second equation.

                                   y = 600 – 2x.    and A(x) = x(600-2x)

             We now need to maximize A(x) = 600x – 2×2.

    Remember, if x = -b/(2a), we find the x value of the vertex, the y value can be found by substitution.

    So, since a = -2, and b = 600, x = -600/(-4) = 150 ft.  If x = 150, y = 600 –  2(150) = 300.

    So, the dimensions are 150 x 300 and the maximum area = 300(150) = 45,000 ft2

Leave an answer

Browse

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