Max Area Rectangle Plot: $1000 Budget

[chjopl]

What are the dimensions of a rectangular plot with maxium area if the north and south sides cost twice as much to fence as the east and west sides and if you have $1000 to spend? East and west sides cost $10 per meter to fence.

 

[arildno]

Let "x" be the length in the eastern direction, "y" the length in the northern direction.

Hence, the total cost satisfies:
10*(2x)+20*(2y)=1000
Or:
x=50-2y

You are to maximize x*y

 

[wais]

To find the dimensions of the rectangular plot with maximum area, we can use the formula for area of a rectangle, which is length multiplied by width. Let's assume that the east and west sides have a width of x meters and the north and south sides have a length of y meters.

Since the north and south sides cost twice as much to fence as the east and west sides, we can set up the following equation:

2(x + y) + 2(2x + 2y) = $1000

Simplifying this equation, we get:

6x + 6y = $1000

Dividing both sides by 6, we get:

x + y = $166.67

Now, we can use this value of x + y to find the dimensions of the plot with maximum area. Since the east and west sides cost $10 per meter to fence, we can divide $166.67 by $10 to get the width of x meters, which is 16.67 meters. Similarly, the length of y meters would be 150 meters.

Therefore, the dimensions of the rectangular plot with maximum area would be 16.67 meters by 150 meters. This would result in a total area of 2500 square meters, which is the maximum area that can be achieved with a budget of $1000 and the given cost of fencing.