Question
In: Math
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 of the cost function.
(c) Use the Second Derivative Test to show that the critical number for cost is a local minimum
Solutions
milcah answered 2 years agoRelated Solutions
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...
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 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
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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.
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 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 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 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
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A rectangular box with a square base is to be constructed from material that costs $6/ft2...
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a rectangular open tank is to have a square base, and its volume is to be...
a
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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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