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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 $8 per linear foot to install and the farmer is not willing to spend more than $4000, find the dimensions for the plot that would enclose the most area. (enter the dimensions as a comma separated list. ).

Respuesta :

The results are x = 125 feet and y = 250/3. Plots are a useful tool for summarizing data in an appealing way and visually portraying it.

Inefficient plotting makes it appear complicated, though. Several libraries are available in Python's matplotlib for the purpose of representing data. Assume that x is the length of the fence's northern section (which runs parallel to the north wall) and y is the length of the fence's western and eastern sections.

In addition, the farmer has $4000 available for purchase, therefore we can write 8x + 8y + 4y = 4000.

8x + 12y = 4000

Consequently, we may state,

Area A = x + y is known.

Since A"(x) is always less than 0, we can conclude that x = 125 is a maximum point using the second derivative test.

Hence, we can state that the dimensions for the plot with the greatest area would be x = 125 feet and y = 250/3 feet.

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