4. A cardboard box without a lid is to have a volume of 32,000 cm³. Find the dimensions that minimizes the amount of cardboard used.

Q: 8. Find the dimensions of a rectangle with area 1000 m² whose perimeter is as small as possible.

A:

Q: 3. Find the dimensions of a open topped box that maximizes the volume with the constraint that the…

A: We need to find dimension of an open box that maximizes the volume.

Q: A piece of wire 22 m long is cut into two pieces. One piece is bent into a square and the other is…

A:

Q: A box with a square base and open top must have a volume of 55296 cm. We wish to find the dimensions…

A:

Q: 2. Suppose an airline policy states that all baggage must be rectangle-shaped with the sum of the…

A: We first calculate the side of square box then calculate its volume. Using formula Volume of cube…

Q: 4.1- You are building five identical pens adjacent to each other with a total area of 1000 m², as…

A: Given, Five identical pens are given below.

Q: A piece of wire 18 m long is cut into two pieces. One piece is bent into a square and the other is…

A: Let x m make a square.So each side= x/4 mArea of the square = (x/4)^2= x^2/16 m^2

Q: We are designing a poster to contain 120 cm2 of printing with a 4-centimeter wide margin at the top…

A: Given: We are designing a poster to contain 120 cm2 of printing with a 4-centimeter wide margin at…

Q: 1. A farmer intends to make four identical rectangular pens each with an area of 100 m? as shown in…

A:

Q: You are designing a rectangular poster to contain 50 in2 of printing with a 4-in. margin at the top…

A: Let 'x' be the height of the whole poster and 'y' be the width of the poster.Area = Total amount of…

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: A worker is to construct an open rectangular box with a square base and a volume of 128 ft. If…

A:

Q: Given a closed box with surface area = 16 and a square bottom, what value of x will maximize the…

A:

Q: A box with a square base and open top must have a volume of 78732 cm'. We wish to find the…

A: We know that the volume of the box with square base x cm and height h cm is given byV=x2hThe amount…

Q: a. A rectangular pen is built with one side against a bam. If 1100 m of fencing are used for the…

A: x=width  y=length  perimeter is given by p=2x+y here we have p=1100 1100=2x+y y=1100-2x . the area…

Q: A window is being built and the bottom is a rectangle and the top is a semicircle. If there is 12…

A:

Q: You are designing a rectangular poster to contain 50 in' of printing with a margin at the top and…

A:

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

A: Since the base is square, let the three-dimensional be x, x and y. Since they are lengths x,y,>0…

Q: 2. Find the dimensions of a rectangle with perimeter 100 m whose area is as large as possible? Find…

A: Here we have to find the dimensions of w rectangle with perimeter 100m whose area is as large as…

Q: 1. A farmer wants to fence in a field and divide it into four side by side, equal areas. If he wants…

A: From the given data And, xy=8000&f(x,y)=2x+5y is the parimeter to minimize.

Q: Suppose the farmer makes the rectangular holding pen using an existing fence for one side. What…

A: Let the farmer makes the rectangular holding pen using an existing fence for one side.  let the…

Q: 5) The hypotenuse of a right triangle is 12 cm in length. Calculate the measures of the unknown…

A: To find the dimensions of given triangle such that it has maximum area.

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: 1. The minimum possible perimeter for a rectangle with an area of 529 m² is

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Coca-Cola wants to minimize the production costs of its cans. Assuming the cans are the shape of a…

A:

Q: A rectangular corral of 96 square meters is to be fenced off and then divided by a fence into two…

A: We use second derivative test to find dimensions where amount of fencing is minimum

Q: A piece of wire 8 m long is cut into two pieces. One piece is bent into a square and the other is…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 14. A box with a square base and open top must have a volume of 32,000 cm³. Find the dimensions of…

A:

Q: Three equally sized corrals are constructed next to a river. if the area to be enclosed is 19600…

A: Use concept of minimizing of fencing

Q: 13. A farmer wants to fence in an area of 1.5 million square feet in a rectangular field and then…

A:

Q: A wire b is cut into two pieces. One piece is bent into an equilateral triangle and the other is…

A:

Q: Of all rectangles with area 400 in2, what are the dimensions of the one with the minimum perimeter?…

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Q: Suppose we have 45 m² of material to build a box with a square bottom and no top. What dimensions…

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Q: what dimensions of the box will minimize its cost of construction? What is the minimal cost?

A: Let l, b, h be the length, breadth, and height of the rectangular box. Then the area of the 4 side…

Q: You’re building five identical pens adjacent to each other with a total area of 1000 m^2, as shown…

A:

Q: A farmer wants to fence an area of 600 square feet in a rectangular field and then divide it in half…

A: Given that, A farmer wants to fence an area of 600 square feet in a rectangular field. After that,…

Q: ndscape architect wished to enclose a rectangular garden on one side by a brick wall costing $40/ft…

A:

Q: 18. A farmer intends to make four identical rectangular pens each with an area of 100 m² as shown in…

A:

Q: 5., You are building TWO identical pens adjacent to each other with a total area of 100 m², as shown…

A: Let's solve 5th question, dimensions for minimize the amount of fencing.

Q: 13. Find the dimensions of a rectangle with area 1000 m² whose perimeter is as small as possible.

A: Given: Area of the rectangle is 1000 m2.

Q: A piece of wire 27 m long is cut into two pieces. One piece is bent into a square and the other is…

A:

Q: You are tasked with constructing a rectangular box with a square base, an open top, and a volume of…

A:

Q: A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing…

A:

Q: A piece of wire 15 m long is cut into two pieces. One piece is bent into a square and the other is…

A: Given A piece of wire 15 m long is cut into two pieces. One piece is bent into a square and the…

Q: A cardboard box without a top is to have a volume of 32,000 cm3 . Find the dimensions that minimize…

A:

Q: 2. b. A farmer wants to fence an area of 1.5 million square feet in a rectangular field and then…

A: Given: Fence area =1.5 million square feet

Q: A piece of wire 6 m long is cut into two pieces. One piece is bent into a square and the other is…

A: We need to find the combined area of square & triangle & where it is maximum