Question
In: Math
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?
Solutions
milcah answered 2 years agoRelated Solutions
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 rectangular tank with a square base, an open top, and a volume of 1372 ft...
A rectangular tank with a square base, an open top, and a
volume of 1372 ft cubed is to be constructed of sheet steel. Find
the dimensions of the tank that has the minimum surface area.
A box with a square base and open top must have a volume of 32000 cm3....
A box with a square base and open top must have a volume of
32000 cm3. We wish to find the dimensions of the box that minimize
the amount of material used.
Find the following:
1. First, find a formula for the surface area of the box in terms
of only x, the length of one side of the square base. [Hint: use
the volume formula to express the height of the box in terms of x.]
Simplify your formula...
An open-top rectangular box is being constructed to hold a volume of 400 in3. The base...
An open-top rectangular box is being constructed to hold a
volume of 400 in3. The base of the box is made from a
material costing 7 cents/in2. The front of the box must
be decorated, and will cost 10 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:
Depth:
Height:
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...
A box with a square base and open top must have a volume of 32000 cm^3....
A box with a square base and open top must have a volume of
32000 cm^3. Find the dimension of the box that minimize the amount
of material used. (show all work)
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 open tank is to have a square base, and its volume is to be...
a
rectangular open tank is to have a square base, and its volume is
to be 125 cubic metrrs. the cost per square meter for the bottom is
$24 and for the sides is $12. find the dimensions of the tank for
which the cost of the material is to be the least. what is the
least cost?
Suppose a tin box is to be constructed with a square base, an open top and...
Suppose a tin box is to be constructed with a square base, an
open top and a volume of 32 cubic inches. The cost of the tin to
construct the box is $0.15 per square inch for the sides and $0.30
per square inch for the base.
The minimized cost of the tin box is:
A. $3.50
B. $$4.82
C. none of the answers
D. $9.07
E. $$\$0$$
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