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?

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)

              = + 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.

your answer would be 12