Suppose that a rectangle has an area of A. Find the dimensions that minimize the perimeter. Show that this really is a minimum.

Q: An open-top box is to be made from a 20 in by 30 in piece of cardboard by removing a square from…

A: Let each side of the square cut-off from each corner be x in. then the length of the base of the box…

Q: If a rectangle has dimensions x and y, then we must maximize the area A = xy. Since the perimeter is…

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Q: a. A rectangular pen is built with one side against a barn. If 1500 m of fencing are used for the…

A: Note:- As per our guidelines, we'll answer the first one as both are different question. Please…

Q: Suppose there is a rectangle with length L and width W (W < L) (in inches that has an area of 324…

A: The area of rectangle is given by A=length×width and perimeter is given by P=2Length+width.

Q: a. A rectangular pen is built with one side against a barn. If 200 m of fencing are used for the…

A: As per the guidelines we are supposed to answer only first question and rest can be reposted..

Q: If an isosceles triangle has a fixed perimeter P, find the dimensions that maximize the area. Your…

A: Given: An isosceles triangle is given with perimeter P. The objective is to find the dimensions of…

Q: 3] Use Lagrange multiplier to find the dimensions that will maximize the area for rectangle whose…

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Q: Of all numbers whose sum is 50, find the two that have the maximum product. That is, maximize Q =…

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Q: A rectangular corral of 726 square meters is to be fenced off and then divided by a fence into two​…

A: Given problem is : A rectangular corral of 726 square meters is to be fenced off and then divided…

Q: A company sells chocolate in rectangular boxes whose volume is 120cm^3. For display purposes, the…

A: Given that the volume of rectangular boxes is 120cm . Then length of the box is three times the…

Q: Show that the problem B symmetric minimize || B A ll subject to Be R is solved by A + AT B= %3D

A: To show that the problem minimizeB∈ℝn×n∥B-A∥F subject to B being symmetric is solved by B=A+AT2

Q: Of all numbers whose sum is 46, find the two that have the maximum product. That is, maximize Q = xy…

A: Given ,           x+y=46           Maximize , Q=xy

Q: A piece of sheet metal is rectangular, 5 feet wide and 8 feet long. Congruent squares are to be cut…

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Given ScZand IS -a, what is the maximum value of x+y:x.YESAX+Y1?

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Q: Use the method of Lagrange multipliers to find the dimensions of a rectangle with perimeter p and…

A: It is given that the perimeter is p and it has maximum area. Let the dimensions of the rectangle be…

Q: Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: A…

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Q: Find the dimensions of a rectangular box of volume 1000cubic inches for which the sum of the…

A: Let x,y,z be the length, breadth and the height of the rectangular boxxyz=1000  and the sum…

Q: 3] Use Lagrange multiplier to find the dimensions that will maximize the area for rectangle whose…

A: Using Lagrange multiplier to find the dimension of rectangle whose area is maximum

Q: Of all numbers whose sum is 52, find the two that have the maximum product. That is, maximize Q = xy…

A: Given, Q=xy                        ...(1) Where x+y=52⇒y=52-x                            ...(2)

Q: Find the length L and width W (with W less than or equal to L) of the rectangle with area of 198…

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Q: Given the area of a rectangle is A = LW. If three sides of the rectangle are fixed, for example, 2VW…

A: Given:- Given the area of a rectangle is A = LW If three sides of the rectangle are fixed, for…

Q: 13. Of all numbers whose difference is 6, find the two that have the minimum product.

A: Let x and y be such numbers. x-y=6 P=xy. Substitute x=6+y in P=xy and obtain that P=y6+y=6y+y2.

Q: 2. Find the length and width of a rectangle that has an area of 800 square feet and whose perimeter…

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Q: Find positive numbers x and y such that x + y = 48 and 5x2y + 10 is maximized.

A: Given that, x + y= 48 y = 48 - x ................... (1) The function is: f(x, y) = 5x2 y+ 10 f(x) =…

Q: Use Lagrange multipliers to find the dimensions of a rectangular box with largest volume if the…

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Q: Find two positive integers such that their sum is 10, and minimize the sum of squares.

A: Given  two positive integers such that their sum is 10, To minimize the sum of squares

Q: Suppose an airline policy states that all baggage must be box-shaped with a sum of length, width,…

A: the length of the square end edge is =?                                     box height is =? the…

Q: Suppose there is a rectangle with length L and width W (W < L) (in inches) that has an area of 324…

A: Given: Area = 324 sq.in             L x W=324             L=324W Perimeter P=2(L+W)     Substituting…

Q: A rancher plans to make four identical and adjacent rectan- gular pens against a barn, each with an…

A: Let the width of each pen be x and the length of each pen be y. As the pens are rectangular thus the…

Q: find the minimum value of

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Q: A rectangular corral of 726 square meters is to be fenced off and then divided by a fence into two…

A: I use second derivative test to find out dimensions where amount of required fencing minimum

Q: Use the method of Lagrange multipliers to find a relative minimum

A: Lagrange multiplier :

Q: The upper right-hand corner of a piece of paper, 12 in. by8 in., as in the figure, is folded over to…

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Q: Suppose we find x =2 and y = 6 to be the proposed dimensions of a rectangle that minimize its area.…

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Q: 3. Prove that of all rectangles with a given area, the one with smallest perimeter is a square. (Let…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the length and width of a rectangle that has an area of 75 square feet and a minimum perimeter.…

A: We have to find length and width of the rectangle.

Q: A city is setting up community garden plots for residents living in apartments. The plots will be…

A: Given area of each plot = 32m2 cost of fencing between lots = $5/m cost of fencing around entire…

Q: Find the maximum area of a rectangle inscribed under f(x)=16-x2 and the x axis

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Q: A city is setting up community garden plots for residents living in apartments. The plots will be…

A: let length of each plot be x and width of each plot be y also length is along x-axis and width is…

Q: A rectangular corral of 600 square meters is to be fenced off and then divided by a fence into two…

A: Given the area of the rectangle.

Q: Find the length and width of a rectangle that has an area of A square centimeters and a minimum…

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Q: According to postal regulations, a carton is classified as oversized if the sum of its height and…

A: NOTE- I have solved the second question as we are allowed to solve only one question in one session.…

Q: A farmer is is building a fence to enclose a rectangular area against an existing wall, shown in the…

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Q: The minimum value of Duf(x, y) is ||Vf(x, y)||. Select one: O True False

A: The properties of gradient: If z is a function of two variables x and y then assume  fx and fy  are…

Q: B) Use Lagrange multipliers to find the dimensions of the closed circular cylinder of smallest…

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Q: The are of a rectangle is 100 cm2 and one of its sides is x cm. Find the minimum perimeter possible.

A: Let us consider a rectangle with length l unit, breadth b unit Then area of this rectangle= lb…

Q: Suppose the labor cost (in dollars) for manufacturing a camera can be approximated by L(x.y) =x +y -…

A: Given: Suppose the labor cost in dollars for manufacturing a camera can be approximated by Lx,…

Q: A poster is being designed that is to contain 150 in of printed material with margins of 2 inches at…

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Q: A rectangular building covering 6,000m2 is to be built on a lot as shown in the figure. If the…

A: Minimize area