Answer:
(150 feet,75 feet)
Step-by-step explanation:
Let
Length of rectangle pasture,l=y
Breadth of rectangle pasture,b=x
Fencing used=300ft
Fencing used=2x+y
300=2x+y
y=300-2x
Area of rectangle pasture=xy
[tex]A=x\times (300-2x)[/tex]
[tex]A=300x-2x^2[/tex]
Differentiate w.r.t x
[tex]\frac{dA}{dx}=300-4x[/tex]
[tex]\frac{dA}{dx}=0[/tex]
[tex]300-4x=0[/tex]
[tex]4x=300[/tex]
[tex]x=\frac{300}{4}=75[/tex]
Again, differentiate w.r.t x
[tex]\frac{d^A}{dx^2}=-4<0[/tex]
Hence, the area is maximum at x=75
Width of rectangle pasture,x=75 feet
Length of rectangle pasture,l=300-2(75)=150 feet
Dimension of rectangle pasture=(l,b)=(150 feet,75 feet)
