Question
In: Math
A closed rectangular box of volume 324 cubic inches is to be made with a square...
A closed rectangular box of volume 324 cubic inches is to be made with a square base. If the material for the bottom costs twice per square inch as much as the material for the sides and top, find the dimensions of the box that minimize the cost of materials.
Solutions
milcah answered 2 years agoRelated Solutions
A closed rectangular container with a square base is to have volume of 36,000 cubic centimeters....
A
closed rectangular container with a square base is to have volume
of 36,000 cubic centimeters. The material for the top and bottom of
the container will cost $0.10 per square centimeter, and the
material for the sides will cost $0.20 per square centimeter. Find
the dimensions with the least cost.
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...
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...
create a speaker box with a volume of 14400 cubic inches. The box will be used...
create a speaker box with a volume of 14400 cubic
inches. The box will be used for speakers of various
sizes. The speaker box must have a square base and minimal surface
area ( prior to cutting holes for the speakers ). Find the box’s
dimensions. Your must construct a diagram [ V = LWH ]
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 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
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 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 cereal box, in the shape of a rectangular prism and with a closed top, is...
A cereal box, in the shape of a rectangular prism and with a
closed top, is to be
constructed so that the base is twice as long as it is wide. Its
volume is to be 8000cm3。
Find the dimensions that will minimize the amount of cardboard
required to make the box.
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