Max Area Rectangle Plot: $1000 Budget

In summary, a max area rectangle plot is a rectangular piece of land with the largest possible area within a given budget constraint. The maximum area is calculated by dividing the budget by the cost per unit area of the land and considering factors such as location, shape, and terrain. The maximum area can change over time due to various factors and there may be limitations when trying to find a plot with a $1000 budget. Flexibility and considering alternative options may be necessary in these cases.
  • #1
chjopl
21
0
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.
 
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  • #2
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
 
  • #3

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.
 

1. What is a max area rectangle plot?

A max area rectangle plot is a rectangular piece of land that has the maximum possible area within a given budget constraint. In other words, it is a plot of land that can be purchased for a specific budget and has the largest possible area within that budget.

2. How is the max area of a rectangle plot calculated?

The max area of a rectangle plot is calculated by dividing the budget by the cost per unit area of the land. This gives the maximum number of units of area that can be purchased within the budget. The length and width of the rectangle can then be determined by finding the square root of the maximum area.

3. What factors should be considered when choosing a max area rectangle plot?

Some factors to consider when choosing a max area rectangle plot include the location, shape, and terrain of the land. The cost per unit area may also vary depending on the location and type of land. It is important to also consider any additional costs such as taxes and fees that may impact the total budget.

4. Can the max area of a rectangle plot change over time?

Yes, the max area of a rectangle plot can change over time due to various factors such as changes in land prices, inflation, and availability of land. It is important to regularly reassess and adjust the budget and other factors when considering a max area rectangle plot.

5. Are there any limitations to finding a max area rectangle plot with a $1000 budget?

Yes, there may be limitations when trying to find a max area rectangle plot with a $1000 budget, depending on the location and availability of land. The cost per unit area may also vary greatly, making it difficult to find a plot with the desired maximum area within the given budget. It is important to be flexible and consider alternative options in such cases.

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