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Define the term unconstrained optimization?

Felix Fitzgerald 2022-08-27

What is the largest area that can be fenced off of a rectangular garden if it will be fenced off with 220 feet of available material?

dyin2be0ey 2022-08-22

A farmer wants to fence an area of 6 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. How can he do this so as to minimize the cost of the fence?

ceriserasb6 2022-08-21

How do you find the point on the the graph $y = \sqrt{x}$ which is plosest to the point (4,0)?

Jazmin Clark 2022-08-19

How do you optimize $f (x, y) = x^{2} - 3 y^{2}$ subject to $x^{3} - y^{2} = 8$ ?

Leyla Bishop 2022-08-19

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola $y = 6 - x^{2}$ . What are the dimensions of such a rectangle with the greatest possible area? thanks for any help!?

Mehlqv 2022-08-16

What is a tight lower bound to $\sum_{i = 1}^{n} \frac{1}{a + x_{i}}$ under the restrictions $\sum_{i = 1}^{n} x_{i} = 0$ and $\sum_{i = 1}^{n} x_{i}^{2} = a^{2}$ ?
Conjecture: due to the steeper rise of $\frac{1}{a + x}$ for negative $x$ , one may keep those values as small as possible. So take $n - 1$ values $x_{i} = - q$ and $x_{n} = (n - 1) q$ to compensate for the first condition. The second one then gives $a^{2} = \sum_{i = 1}^{n} x_{i}^{2} = q^{2} ((n - 1)^{2} + n - 1) = q^{2} n (n - 1)$ . Hence,
$\sum_{i = 1}^{n} \frac{1}{a + x_{i}} \geq \frac{n - 1}{a (1 - 1 / \sqrt{n (n - 1)})} + \frac{1}{a (1 + (n - 1) / \sqrt{n (n - 1)})}$
should be the tight lower bound.

Lokubovumn 2022-08-13

How do you find the point on the curve $y = 2 x^{2}$ closest to (2,1)?

Nica2t 2022-08-12

Let's say I have $480 to fence in a rectangular garden. The fencing for the north and south sides of the garden costs $10 per foot and the fencing for the east and west sides costs $15 per foot. How can I find the dimensions of the largest possible garden.?

popljuvao69 2022-08-12

A rectangle is constructed with it's base on the x-axis and the two of its vertices on the parabola $y = 49 - x^{2}$ . What are the dimensions of the rectangle with the maximum area?

tuanazado 2022-08-11

How do you find the dimensions that minimize the amount of cardboard used if a cardboard box without a lid is to have a volume of $8, 788 {(c m)}^{3}$ ?

Alexandra Richardson 2022-07-23

How do you find the area of the largest isosceles triangle having a perimeter of 18 meters?

vangstosiis 2022-07-22

A sodium chloride crystal in the shape of a cube is expanding at the rate of 60 cubic microns per second. How fast is the side of the cube growing when the volume is 1000 cubic microns?

Markus Petty 2022-07-20

You are designing a rectangular poster to contain 50 in^2 of printing with a 4-in. margin at the top and bottom and a 2-in margin at each side. What overall dimensions will minimize the amount of paper used?

Lexi Mcneil 2022-07-19

How do you find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle of side L if one side of the rectangle lies on the base of the triangle?

daniel suriya2022-07-19

valtricotinevh 2022-07-17

An open top box is to be constructed so that its base is twice as long as it is wide. Its volume is to be 2400cm cubed. How do you find the dimensions that will minimize the amount of cardboard requiblack?

Glenn Hopkins 2022-07-16

How do you optimize $f (x, y) = x y - x^{2} + e^{y}$ subject to $x - y = 8$ ?

Optimization in calculus stands for the process where you aim to find the maximum and minimum values by the provided constraints. This is exactly where the calculus is implemented. You may either go with the equations or the word problem as most answers do. The trick is to find the maximum profit for something or the minimum time it will take to complete an operation. It’s what makes optimization in calculus so important. See several answers that are provided below to use the data as the template for your assignment. It will help you t find the most efficient solutions.

Multivariable calculus

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