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?A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his
Chapter 4, Problem 15(choose chapter or problem)
A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $20 per linear foot to install and the farmer is not willing to spend more than $5000, find the dimensions for the plot that would enclose the most area.
Questions & Answers
QUESTION:
A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $20 per linear foot to install and the farmer is not willing to spend more than $5000, find the dimensions for the plot that would enclose the most area.
ANSWER:Step 1 of 7
Let the length (adjacent to the Barn) of the rectangular plot be y and width be x. It has been stated that. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbour who will split the cost of that portion of the fence. Therefore, the perimeter of the plot that need to be fenced will be
\(\begin{array}{l}
=y+x+\frac{1}{2} x \\
=y+\frac{3}{2} x
\end{array}\)