The fence around Wayne Manor is going to be replaced. No fence will be required on the side lying along Gotham River. If the new wrought iron fence costs $12 per meter for the side parallel to the river, and $4 per meter for the other two sides, find the dimensions of the maximum area that can be enclosed by the fence if Bruce Wayne cannot spend more than $3600.

Step-by-step explanation:

Let the side parallel to the river be x meter and the other two sides be of y meter, then

The area of the rectangle is

Substitute into to express the area in a single variable x as,

Differentiate A(x) with respect to x and equate to zero as,

x=150

Here, at is maximum

Therefore, the dimension is:

Length of side parallel to the river: x=150 m.

Length of other two side: m.

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