# Calculus

You are an engineer in charge of designing the dimensions of a box-like building. The base is rectangular in shape with width being twice as large as length. (Therefore so is the ceiling.) The volume is to be 1944000 m3. Local bylaws stipulate that the building must be no higher than 30 m. Suppose the walls cost twice as much per m2 as the ceiling, and suppose the floor (i.e.base) costs nothing. Find the dimensions of the building that would minimize the cost.

1. 0
2. 1
1. The answer might be easy if you told us the minimum height requirement.

Since the ceiling is cheaper, the lower the height, the cheaper it will be.

Once we know that, the squarer the building, As equal as possible in length & width, the smaller the perimeter and therefore the less m2 of walls.

Hope this helps

1. 0
posted by ali

## Similar Questions

1. ### math - Calc optimization

You are an engineer in charge of designing the dimensions of a box-like building. The base is rectangular in shape with width being twice as large as length. (Therefore so is the ceiling.) The volume is to be 1944000 m3. Local
2. ### Math Pre-Calc 12

A box has a Square base. The Perimeter of the base plus the height is 120cm. What is the max volume of this box, and what are the dimensions of the this maximized box.
3. ### math

A box with a square base and no top is to hold 32in^3. Find the dimensions that require the least building material nevermind i got it
4. ### calculus

An open box is to be constructed so that the length of the base is 4 times larger than the width of the base. If the cost to construct the base is 5 dollars per square foot and the cost to construct the four sides is 3 dollars per
5. ### math

A box with a rectangular base and rectangular sides is to be open at the top. It is to be constructed so that its width is 8 meters and its volume is 72 cubic meters. If building this box costs \$20 per square meter for the base
6. ### math

An Engineer is designing a bolt to fit a new machine. The bolt was the shape of a hexagon with a cymetrical hole in its center. The greatest distance across the bolt is 1.25cm, and the depth of 0.5cm. The diameter of the whole is
7. ### Pre Cal

find the surface area of a box of hieght h whose base dimensions are p and q, and that satisfies either one of the following conditions: a) the box is closed. b) the box has an open top. c) the box has an open top and a square
8. ### MATH

E LARGEST PYRAMID IN THE U.S. IS THE LUXUR HOTEL IN VEGAS. THE VOLUME OF THIS HOTEL IS 28,933,800 OR ABOUT 29 MILLION CUBIC FEET. THE HEIGHT OF THE PYRAMID IS 148 FEET LESS THAN THE LENGTH OF THE BUILDING. THE BASE OF THE BUILDING
9. ### Calculus 1-Optimization

A box with a square base and open top must have a volume of 4,000 cm^3. Find the dimensions of the box that minimize the amount of material used. sides of base cm height cm
10. ### Pre-Cal

A box with a square base and an open top is constructed from 5400 cm^2 of cardboard. Find the dimensions of the largest possible box. I know the answer is : base lenght - 42.4 cm height- 21.2 cm please help me, thank you so much

More Similar Questions