Please state the closed interval domain for the optimization function and carry
ID: 2849566 • Letter: P
Question
Please state the closed interval domain for the optimization function and carry out the closed-interval method. Thank you!
1. A landowner uses 3600 meters of fence to create a large rectangular enclosure subdivided into three adjacent rectangular sections, as shown. Find the dimensions x and y that aximize area of the entire enclosure, and find this maximum arca. Area of a rectangle is the product of its length and width. All segments shown are fenced. lo earn full credit, state the closed-interval domain for the optimization function and carry out the "closed-interval method." Answer: If x= Answer If x meters and y- meters, the total area of the enclosure will be square meters.Explanation / Answer
Area of the fiels = xy
==> f(x,y) = xy
given total length of fence = 3600 m
==> 2x + 4y = 3600
==> x +2y = 1800
==> 2y = 1800 -x
==> y = 900 - (x/2)
Domain of x = [0 , 1800] since x,y cannot be negative
f(x,y)= xy
==> f(x) = x(900 - (x/2))
==> f(x) = 900x -x2/2
For maximum or minimum f '(x) = 0
==> 900 - x = 0
==> x = 900
==> y = 900 - (900/2) = 450
Hence maximum area = (900)(450) = 405000 square meters