Question

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.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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.
A company plans to manufacture a rectangular box with a square base, an open top, and...
A company plans to manufacture a rectangular box with a square base, an open top, and a volume of 404 cm3. The cost of the material for the base is 0.5 cents per square centimeter, and the cost of the material for the sides is 0.1 cents per square centimeter. Determine the dimensions of the box that will minimize the cost of manufacturing it. What is the minimum cost?
An open rectangular box (no top) is formed with a square base and rectangular sides so...
An open rectangular box (no top) is formed with a square base and rectangular sides so that the total volume enclosed is 475 cu. ft. What is the smallest amount of material (area) that can form such a box?
An open-topped box is to have a square base and a volume of 10 ?3. The...
An open-topped box is to have a square base and a volume of 10 ?3. The cost per square meter of material is $5 for the bottom and $2 for the four sides. Let ? be the length of the base of the box and ℎ be the height of the box. Let ? be the total cost of material required to make the box. a. Express ? as a function of ? and find its domain. b. Find the...
a rectangular box with an open top and one partition is to be constructed from 288...
a rectangular box with an open top and one partition is to be constructed from 288 inches of cardboard.Find the dimensions that result in a box with largest possible volume.
An open-top rectangular box is being constructed to hold a volume of 300 in3. The base...
An open-top rectangular box is being constructed to hold a volume of 300 in3. The base of the box is made from a material costing 8 cents/in2. The front of the box must be decorated, and will cost 12 cents/in2. The remainder of the sides will cost 2 cents/in2. Find the dimensions that will minimize the cost of constructing this box. Front width: _______ in. Depth: ________ in. Height: ________ in.
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
A rectangular box is to have a square base and a volume of 16 ft3. If...
A rectangular box is to have a square base and a volume of 16 ft3. If the material for the base costs $0.14/ft2, the material for the sides costs $0.06/ft2, and the material for the top costs $0.10/ft2, determine the dimensions (in ft) of the box that can be constructed at minimum cost. (Refer to the figure below.) A closed rectangular box has a length of x, a width of x, and a height of y.
Minimizing Packaging Costs A rectangular box is to have a square base and a volume of...
Minimizing Packaging Costs A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base costs $0.28/ft2, the material for the sides costs $0.10/ft2, and the material for the top costs $0.22/ft2, determine the dimensions (in ft) of the box that can be constructed at minimum cost. (Refer to the figure below.) A closed rectangular box has a length of x, a width of x, and a height of y. x...
A box with a square base and an open top must have a volume of 864...
A box with a square base and an open top must have a volume of 864 cm^3. Find the dimensions of the box that minimize the amount of material used.