Question

Show your complete solution. 1. Use Lagrange Multiplier to determine the dimensions of a rectangular box,...

Show your complete solution.

1. Use Lagrange Multiplier to determine the dimensions of a rectangular box, open at the top, having a volume of 32 cubic feet and requiring the least amount of material for its construction.

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let x,y,z denote the dimensions of a rectangular box open at top. If the function V(x,y,z)=a...
Let x,y,z denote the dimensions of a rectangular box open at top. If the function V(x,y,z)=a gives the volume, where a= 24,  find the minimum amount  of material required for its construction.
a rectangular box with no top and six compartments is to be made to hold a...
a rectangular box with no top and six compartments is to be made to hold a volume of 96 cubic inches. which of the following is the least amount of material used in its construction
Use Lagrange multipliers to find the dimensions of the rectangular box of maximum volume, with faces...
Use Lagrange multipliers to find the dimensions of the rectangular box of maximum volume, with faces parallel on the coordinate planes, that can be inscribed in the first octant of the ellipsoid 4x^2 + y^2 +4z^2=192
Show work, draw a picture, label your variables. (4pts) We want to construct a box whose...
Show work, draw a picture, label your variables. (4pts) We want to construct a box whose base length is 4 times the base width. The material used to build the top and bottom cost $10 sq foot and material used to build the sides cost $6 sq foot. If the box must have a volume of 60 cubic feet, determine the dimensions that will minimize the cost to build the box and find the minimum cost box. * Give your...
A large shipping crate is to be constructed in a form of a rectangular box with...
A large shipping crate is to be constructed in a form of a rectangular box with a square base. It is to have a volume of 441 cubic feet. The material for the base of the crate is steel that costs $6 per square foot, the rest of the crate is constructed out of wood. The wood for the top of the crate is less expensive at $3 per square foot and the sides will be constructed from the wood...
A rectangular box with a square base has a volume of 4 cubic feet. The material...
A rectangular box with a square base has a volume of 4 cubic feet. The material for the bottom of the box costs $3 per square foot, the top costs $2 per square foot, and the four sides cost $5 per square foot. (a) If x is the side length of the square base, and y is the height of the box, find the total cost of the box as a function of one variable. (b) Find the critical number...
Let’s now complete the “open box” question mentioned in the previous question. Suppose we have 1200in2...
Let’s now complete the “open box” question mentioned in the previous question. Suppose we have 1200in2 of material that we will use to create a box that has a rectangular base (the base may or may not be a square), but no top. What dimensions maximize the volume? (a) Draw a sketch of the box in this question. Appropriately label the relevant information in your sketch. (b) Based on your sketch above, what equation is being maximized? (c) Based on...
1- An open box with a square base is to have a volume of 10 ft3....
1- An open box with a square base is to have a volume of 10 ft3. (a) Find a function that models the surface area A of the box in terms of the length of one side of the base x. (b) Find the box dimensions that minimize the amount of material used. (Round your answers to two decimal places.) 2- Find the dimensions that give the largest area for the rectangle. Its base is on the x-axis and its...
We can experiment with two parallelepipeds (boxes) that are similar in shape. The dimensions of the...
We can experiment with two parallelepipeds (boxes) that are similar in shape. The dimensions of the smaller box are 2 in. x 4 in. x 3 in. The larger box has twice the dimensions of the smaller . Draw and label the large box 1. Surface area (SA) of a box is the sum of the areas of all six sides. Compare the SAs of the two boxes. top or bottom front or back side total surface area small box...
1) A rectangular storage container with an open top is to have a volume of 24...
1) A rectangular storage container with an open top is to have a volume of 24 cubic meters. The length of its base is twice the width. Material for the base costs 15 dollars per square meter. Material for the sides costs 4 dollars per square meter. Find the cost of materials for the cheapest such container. Total cost =________________________ (Round to the nearest penny and include monetary units. For example, if your answer is 1.095, enter $1.10 including the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT