A farmer wants to fence a rectangular corral adjacent to the side of a barn; however, she has only 200 ft of fencing and wants to enclose the largest possible area. See the figure. a .If x represents the length of the corral and y represents the width, explain why the dimensions of the corral are subject to the constraint 2 x + y = 200 . b . The area of the corral is given by A = x y . Use the constraint equation from part ( a ) to express A as a function of x , where 0 < x < 100 . c .Use the function from part ( b ) to find the dimensions of the corral that will yield the maximum area. [ Hint : Find the vertex of the function from part ( b ).]
A farmer wants to fence a rectangular corral adjacent to the side of a barn; however, she has only 200 ft of fencing and wants to enclose the largest possible area. See the figure. a .If x represents the length of the corral and y represents the width, explain why the dimensions of the corral are subject to the constraint 2 x + y = 200 . b . The area of the corral is given by A = x y . Use the constraint equation from part ( a ) to express A as a function of x , where 0 < x < 100 . c .Use the function from part ( b ) to find the dimensions of the corral that will yield the maximum area. [ Hint : Find the vertex of the function from part ( b ).]
Solution Summary: The farmer wants to fence a rectangular corral and has 200ft of fencing to enclose the largest possible area.
A farmer wants to fence a rectangular corral adjacent to the side of a barn; however, she has only 200 ft of fencing and wants to enclose the largest possible area. See the figure.
a.If x represents the length of the corral and y represents the width, explain why the dimensions of the corral are subject to the constraint
2
x
+
y
=
200
.
b. The area of the corral is given by
A
=
x
y
. Use the constraint equation from part (a) to express A as a function of x, where
0
<
x
<
100
.
c.Use the function from part (b) to find the dimensions of the corral that will yield the maximum area.
[Hint: Find the vertex of the function from part (b).]
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