Question
In: Math
A square-bottomed box with no top has a fixed volume of 1000 ft^3 . Determine the...
A square-bottomed box with no top has a fixed volume of 1000 ft^3 . Determine the dimensions of the box that would minimize the amount of material required to make the box. Show the units and justify your answer.
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 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 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.
An open-top rectangular box has a volume of 250 cm 3. The width of the box...
An open-top rectangular box has a volume of 250 cm 3. The width
of the box is 5 cm. The cost is $2/ cm 2 for the base and $1/ cm 2
for the other sides. What is the minimum cost for making the
box?
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...
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 box has a bottom with one edge 7 times as long as the other. If the box has no top and the volume is fixed at ?V, what dimensions minimize the surface area?
A box has a bottom with one edge 7 times as long as the other. If the box has no top and the volume is fixed at ?V, what dimensions minimize the surface area?
dimensions = ________________Enter the dimensions as a comma-separated list, e.g., 3,sqrt(12),8. (Your answer may involve V.)
The top and bottom margins of a poster are 2 cm and the side margins are each 6 cm. If the area of printed material on the poster is fixed at...
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...
Minimizing Packaging Costs If an open box has a square base and a volume of 91...
Minimizing Packaging Costs If an open box has a square base and
a volume of 91 in.3 and is constructed from a tin sheet, find the
dimensions of the box, assuming a minimum amount of material is
used in its construction. (Round your answers to two decimal
places.)
- Height
- Length
-Width
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