Question

In: Advanced Math

We want to design a rectangular box without a lid with a volume of 64000 cm^3....

We want to design a rectangular box without a lid with a volume of 64000 cm^3. Find the dimensions that maximize the surface area. Using Lagrange Multipliers
Can you explain your reasoning pls

Solutions

Expert Solution

ANSWER :

Find the dimension that maximize the surface area.

Let the length =x , width=y, height= z

Toget max surface area we will use

Lagranges multipliers and

so,

Puting this relation is

To get max surface area the direction is

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

A rectangular box without a lid should be made with 12m2 of cardboard. What are the...

A rectangular box without a lid should be made with 12m2 of cardboard. What are the dimensions of the box that maximize the volume? a.) 2m x 2m x 2m b) 1.54m x 1.54m x 0.77m c) 2m x 2m x 1m d) 4m x 4m x 2m

An open-top rectangular box has a volume of 250 cm 3. The width of the box...

An open-top rectangular box has a volume of 250 cm 3. The width of the box is 5 cm. The cost is $2/ cm 2 for the base and $1/ cm 2 for the other sides. What is the minimum cost for making the box?

A rectangular box without a lid is to be made from 12 m^2 of cardboard. Find...

A rectangular box without a lid is to be made from 12 m^2 of cardboard. Find the maximum volume of such a box

We are tasked with constructing a rectangular box with a volume of 1313 cubic feet. The...

We are tasked with constructing a rectangular box with a volume of 1313 cubic feet. The material for the top costs 1010 dollars per square foot, the material for the 4 sides costs 22 dollars per square foot, and the material for the bottom costs 99 dollars per square foot. To the nearest cent, what is the minimum cost for such a box?

A rectangular box with a square base and an open top and a volume of 1ft^3...

A rectangular box with a square base and an open top and a volume of 1ft^3 is to be made. Suppose the material used to build the sides cost $4 per ft^2 and the material used to build the bottom costs $1 per ft^2. Determine the dimensions (i.e. the side-length of the base and the height) of the box that will minimize the cost to build the box. Note: if we let x denote the side-length of the base and...

A company plans to design an open top rectangular box with square base having volume 4...

A company plans to design an open top rectangular box with square base having volume 4 cubic inches. Find the dimension of the box so that the amount of materiel required for construction is minimal. (a) Find the dimension of the box so that the amount of materiel required for construction is minimized. (b) What is the minimized material required for the construction?

A rectangular box with no top is to be made to hold a volume of 32...

A rectangular box with no top is to be made to hold a volume of 32 cubic inches. Which of following is the least amount of material used in its construction? a.) 80 in2 b.) 48 in2 c.) 64 in2 d.) 96 in2

You want to build a rectangular box in such a way that the sum of the...

You want to build a rectangular box in such a way that the sum of the length, width and height is 24 cm. a) Define the equations so that the dimensions of their volume are maximum b) Which of the equations proposed would be the restriction and which function? Explain c) Using the technique you want to calculate maximums and minimums, what are these values? What volume will the box have?

A rectangular box is to have a square base and a volume of 40 ft3. If...

A rectangular box is to have a square base and a volume of 40 ft3. If the material for the base costs $0.35 per square foot, the material for the sides costs $0.05 per square foot, and the material for the top costs $0.15 per square foot, determine the dimensions of the box that can be constructed at minimum cost. = Length Width Height how do i find length width and height

A box with a square base and open top must have a volume of 32000 cm^3....

A box with a square base and open top must have a volume of 32000 cm^3. Find the dimension of the box that minimize the amount of material used. (show all work)

Subjects