Carol has 1,900 ft of fencing to fence in a rectangular horse corral.

label Algebra
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(a) Find a function that models the area A of the corral in terms of the width x of the corral. 

A(x) =

(b) Find the dimensions of the rectangle that maximize the area of the corral. 
width     ft
length     ft
Mar 10th, 2015

Answer:

I call with x the width, and with y the length

so I can write:

2(x+y) = 1900

or

x +y = 950,

then

y = 950 - x

finally:

A(x) = x (950 -x)

in order to answer to the second part, we have to compute the first derivative of A(x)

dA/ dx = 950 - 2x

then  I set dA/dx = 0, and I find x =475, and y = 475.

width = 475 , length = 475

In other words the corral is a square whose side is equal to 475 feet

Mar 10th, 2015

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