Optimization Math Help: Finding Minimum Enclosed Area with Wire Cut

Thread starter fghtffyrdmns
Start date Oct 8, 2009
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Optimization

In summary, the circumference of a circle is 8 - x cm, while the circumference of a square is 16 - x cm.

Oct 13, 2009

Mark44

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You can choose to not make the cut at all, so that you make only a square or only a circle. So the domain of A(x) is {x in the real numbers| 0 <= x <= 8}.

Now finish the problem. Be sure to check x = 0 and x = 8 after you have solved A'(x) = 0. That way you can be sure you have found the absolute maximum area.

<h2> How is optimization math used in finding minimum enclosed area with wire cut?</h2><p>Optimization math is used to find the minimum possible value for a given function. In the case of finding minimum enclosed area with wire cut, optimization is used to determine the dimensions of a rectangle that will enclose the largest possible area with a fixed amount of wire.</p><h2> What is the objective function in this problem?</h2><p>The objective function in this problem is the area of the rectangle, which is calculated by multiplying the length and width of the rectangle. The goal is to maximize this function to find the largest possible area.</p><h2> How do you set up the constraints for this problem?</h2><p>The constraints for this problem are the length of wire available and the fact that the rectangle must have four sides. These constraints can be represented as equations and inequalities, such as 2l + 2w = wire length and l > 0, w > 0, where l is the length and w is the width of the rectangle.</p><h2> What is the process for solving this optimization problem?</h2><p>The process for solving this optimization problem involves setting up the objective function and constraints, and then using techniques such as differentiation and substitution to find the critical points. These critical points are then evaluated to determine the maximum value of the objective function, which corresponds to the dimensions of the rectangle that encloses the largest area with the given amount of wire.</p><h2> Can this problem be solved using calculus?</h2><p>Yes, this problem can be solved using calculus. The optimization techniques used, such as differentiation and substitution, are based on calculus principles. However, there are also other methods, such as geometric reasoning, that can be used to solve this problem without calculus.</p>

FAQ: Optimization Math Help: Finding Minimum Enclosed Area with Wire Cut

How is optimization math used in finding minimum enclosed area with wire cut?

Optimization math is used to find the minimum possible value for a given function. In the case of finding minimum enclosed area with wire cut, optimization is used to determine the dimensions of a rectangle that will enclose the largest possible area with a fixed amount of wire.

What is the objective function in this problem?

The objective function in this problem is the area of the rectangle, which is calculated by multiplying the length and width of the rectangle. The goal is to maximize this function to find the largest possible area.

How do you set up the constraints for this problem?

The constraints for this problem are the length of wire available and the fact that the rectangle must have four sides. These constraints can be represented as equations and inequalities, such as 2l + 2w = wire length and l > 0, w > 0, where l is the length and w is the width of the rectangle.

What is the process for solving this optimization problem?

The process for solving this optimization problem involves setting up the objective function and constraints, and then using techniques such as differentiation and substitution to find the critical points. These critical points are then evaluated to determine the maximum value of the objective function, which corresponds to the dimensions of the rectangle that encloses the largest area with the given amount of wire.

Can this problem be solved using calculus?

Yes, this problem can be solved using calculus. The optimization techniques used, such as differentiation and substitution, are based on calculus principles. However, there are also other methods, such as geometric reasoning, that can be used to solve this problem without calculus.