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

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

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