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Question 2 options: A farmer wants to build a fenced-in pasture for livestock grazing so that it is rectangular shaped, but that one side is located along a pond so that no fence is needed. If the farmer has 4500 feet of fencing, what are the dimensions of the pasture that will provide the maximum grazing area?

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Answer:

Step-by-step explanation:

Let x = length of fenced side parallel to the side that borders the river

    y = length of each of the other two fenced sides  

Then, x + 2y = 4500

<=>  x = 4500- 2y

 

Area = xy = y(4500-2y)

              = [tex]-2y^{2}[/tex] + 4500y

The graph of the area function is a parabola opening downward.

The maximum area occurs when y = -4500/[2(-2)] = 1125

                                              x = 4500-2y = 2250

To maximize the area, the fenced side parallel to the pone be 2250 feet long, while each of the other two fenced sides should be 1125 feet long.

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