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A cylinder shaped can needs to be constructed to hold 600 cubic centimeters of soup. The...
A box with an open top has a length of x centimeters, width of y centimeters,...
A box with an open top has a length of x centimeters, width of y centimeters, height of z centimeters, and fixed volume of 125 cubic centimeters. The box is divided into two equal parts along its height. The bottom part is divided into two equal parts along its length. One of these parts is divided into two equal parts along its width. The sturdy material used for the base of the box costs $4 per square centimeter, and the...
A rectangular box, open at the top, is to have a volume of 1,728 cubic inches. Find the dimension...
A rectangular box, open at the top, is to have a volume of 1,728 cubic inches. Find the dimensions of the box that will minimize the cost of the box if the material of the bottom costs 16 cents per square inch, and the material of the sides costs 1 cent per square inch.
A rectangular box, open at the top, is to have a volume of 1,728 cubic inches. Find the dimensions of the box that will minimize the...
A rectangular box with a volume of 320 cubic feet is to be constructed with a...
A rectangular box with a volume of 320 cubic feet is to be constructed with a square base and top. The cost per square foot for the bottom is 15 cents, for the top is 10 cents and for the sides is 2.5 cents. What dimensions will minimize the cost?
3. This problem revisits the question from Problem Set I about finding the dimensions of a one-liter can that will...
3. This problem revisits the question from Problem Set I about finding the dimensions of a one-liter can that will have the minimum cost. We will now approach it using calculus methods. In class, we found the dimensions of a right circular cylinder (a “can") that has a volume of 1,000 cm3 using the minimum possible material. This assignment changes that problem slightly by seeking the minimum cost for a right circular cylinder whose volume is 1,000 cm3 where the...
A large cylinder (shaped like a tuna can) has top and bottom area A and height...
A large cylinder (shaped like a tuna can) has top and bottom area A and height h, and is made of a uniform material of density ρc. It is floating on a liquid of density ρf . Assume that √ A > h so the cylinder doesn’t tip while the top is facing upwards, and assume that ρc < ρf . (a) What pressure on the bottom of the cylinder would be required to provide enough force to keep the...
3) You are constructing a 12 cubic feet box that is open at the top. The...
3) You are constructing a 12 cubic feet box that is open at the top. The material used to construct the bottom costs $3 per square foot and the material used to construct the sides is $1 per square foot. What dimensions should you use to minimize the cost of the materials? Set up and solve using the LaGrange method.
A square bottomed, open top box is to be constructed to contain a volume of 500cm'....
A square bottomed, open top box is to be constructed to contain a volume of 500cm'. The material for the bottom of the box costs $0.08/cm2 and the material for the four sides costs $0.03/cm2. In this problem you will compute the minimum cost box that can be constructed subject to our constraint. Use r for the length of the sides of the bottom of the box and y for the height of the box.
Background: Optimization. You work for a company that manufactures cylindrical steel drums that c...
Background: Optimization. You work for a company that manufactures cylindrical steel drums that can be used to transport various petroleum products. Your assignment is to determine the dimensions (radius and height) of a drum that is to have a volume of I cubic meter while minimizing the cost of the drum I. The cost of the steel used in making the drum is $3 per square meter. The top and bottom of the im are cut from squares, and all...
Problem 2 A company needs to order the material needed for constructing rectangular crates. The sides of these crat...
Problem 2 A company needs to order the material needed for constructing rectangular crates. The sides of these crates need to be a wire fencing material that can only be cut into whole number lengths and widths in order to properly assemble the crate. The crate is the shape of a right-rectangular prism. The sides of these crates are wire fencing that costs $5 or $6 per square foot (choose one). The top of these crates are made of hardwood...
Hi can you please answer these two questions!! ASAP, Thanks a lot!! :) 1) A rectangular...
Hi can you please answer these two questions!! ASAP, Thanks a lot!! :) 1) A rectangular box is to have a square base and a volume of 24 ft. 3. If the material for the base costs 20 cent/square foot, the material for the sides costs 10 cent/square foot, and the material for the top costs 40 cent/square foot, determine the dimensions of the box that can be constructed at minimum cost. 2) A book designer has decided...
A box with an open top has a length of x centimeters, width of y centimeters, height of z centimeters, and fixed volume of 125 cubic centimeters. The box is divided into two equal parts along its height. The bottom part is divided into two equal parts along its length. One of these parts is divided into two equal parts along its width. The sturdy material used for the base of the box costs $4 per square centimeter, and the...
A rectangular box, open at the top, is to have a volume of 1,728 cubic inches. Find the dimensions of the box that will minimize the cost of the box if the material of the bottom costs 16 cents per square inch, and the material of the sides costs 1 cent per square inch.
A rectangular box, open at the top, is to have a volume of 1,728 cubic inches. Find the dimensions of the box that will minimize the...
3. This problem revisits the question from Problem Set I about finding the dimensions of a one-liter can that will have the minimum cost. We will now approach it using calculus methods. In class, we found the dimensions of a right circular cylinder (a “can") that has a volume of 1,000 cm3 using the minimum possible material. This assignment changes that problem slightly by seeking the minimum cost for a right circular cylinder whose volume is 1,000 cm3 where the...
3) You are constructing a 12 cubic feet box that is open at the top. The material used to construct the bottom costs $3 per square foot and the material used to construct the sides is $1 per square foot. What dimensions should you use to minimize the cost of the materials? Set up and solve using the LaGrange method.
A square bottomed, open top box is to be constructed to contain a volume of 500cm'. The material for the bottom of the box costs $0.08/cm2 and the material for the four sides costs $0.03/cm2. In this problem you will compute the minimum cost box that can be constructed subject to our constraint. Use r for the length of the sides of the bottom of the box and y for the height of the box.
Background: Optimization. You work for a company that manufactures cylindrical steel drums that can be used to transport various petroleum products. Your assignment is to determine the dimensions (radius and height) of a drum that is to have a volume of I cubic meter while minimizing the cost of the drum I. The cost of the steel used in making the drum is $3 per square meter. The top and bottom of the im are cut from squares, and all...
Problem 2 A company needs to order the material needed for constructing rectangular crates. The sides of these crates need to be a wire fencing material that can only be cut into whole number lengths and widths in order to properly assemble the crate. The crate is the shape of a right-rectangular prism. The sides of these crates are wire fencing that costs $5 or $6 per square foot (choose one). The top of these crates are made of hardwood...
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