Question

[-75.54 Points] DETAILS SCALCET8 4.7.018. A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $10 per linear foot to install and the farmer is not willing to spend more than $5000, find the dimensions for the plot that would enclose the most area. (width, length) -

Answer 1

ab x = 125 , Alx) Area = xy y Perimeter BARN ly cost Feueing-> F(x,y) = 2xty Tister fencing cost a 10 (ext) Keing that budget for fencing 500p = '{$(2xty 2x + y = y = Max Max Area = 500 500-2x Area Alary) = xy - A(x) = x (500-20) 500% - 2x2 Max Area =) A'(x) = 0 Af(x) = 500 — 47 0 tot 500-48 x = = 125 A"(*) 500 Y -4 co is Max Area 500 -2(125) 500 250 -) 250 y = that encloses May Area Dircenstions q prot 125, 250 CS Scanned with CamScanner