SOLUTION: I need help with solving this problem. Here is the question: Chris has purchased 50 feet of fencing to build a rectangular pen along the side of a hay barn. Therefore, the barn can

Question 933281: I need help with solving this problem. Here is the question: Chris has purchased 50 feet of fencing to build a rectangular pen along the side of a hay barn. Therefore, the barn can serve as one side of the pen.
a) Determine an algebraic function for the area of the pen.
b) Find the dimensions of the pen that will yield the maximum area.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Chris has purchased 50 feet of fencing to build a rectangular pen along the side of a hay barn. Therefore, the barn can serve as one side of the pen.
a) Determine an algebraic function for the area of the pen.
b) Find the dimensions of the pen that will yield the maximum area.
***
let x=width
let y=length (side facing barn)
2x+y=50
y=50-2x
Area,A=xy=x(50-2x)
A=50x-2x^2
A=-2x^2+50x
complete the square:
A=-2(x^2-25x+(12.5)^2)+312.5
A=-2(x-12.5)+312.5 (algebraic function for the area of the pen)
This is an equation of a parabola that opens down with vertex at (12.5,312.5)
dimensions of pen to yield maximum area of 312 sq ft:
width=12.5 ft
length=50-2x=50-25=25 ft

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