Question

A carpenter wants to construct a closed-topped box whose base length is 2 times the base width. The wood used to build the top and bottom costs $7 per square foot, and the wood used to build the sides costs $6 per square foot. The box must have a volume of 12 cubic feet. What equation could be used to find the smallest possible cost for the box?

Answer #1

Show work, draw a picture, label your variables. (4pts)
We want to construct a box whose base length is 4 times the base
width. The material used to build the top and bottom cost $10 sq
foot and material used to build the sides cost $6 sq foot. If the
box must have a volume of 60 cubic feet, determine the dimensions
that will minimize the cost to build the box and find the minimum
cost box.
* Give your...

We have to build a box that has no top and whose base length is
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the dimensions of the box that will have the greatest volume.

A rectangular box with a square base has a volume of 4 cubic
feet. 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 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. If x is the side length...

A rectangular box with a square base has a volume of 4 cubic
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foot, the top costs $2 per square foot, and the four sides cost $5
per square foot Find the critical number of the cost function.

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...

Gloria would like to construct a box with volume of exactly
55ft3 using only metal and wood. The metal costs $14/ft2 and the
wood cost $5/ft2. If the wood is to go on the sides, the metal is
to go on the top and bottom, and if the length of the base is to be
3 times the width of the base, find the dimensions of the box that
will minimize the cost of construction. Round your answe to the...

A box is contructed out of two different types of metal. The
metal for the top and bottom, which are both square, costs $2 per
square foot and the metal for the sides costs $2 per square foot.
Find the dimensions that minimize cost if the box has a volume of
25 cubic feet. Length of base x= Height of side z=?

Gloria would like to construct a box with volume of exactly
55ft3 using only metal and wood. The metal costs $7/ft2 and the
wood costs $4/ft2. If the wood is to go on the sides, the metal is
to go on the top and bottom, and if the length of the base is to be
3 times the width of the base, find the dimensions of the box that
will minimize the cost of construction. Round your answer to the...

A cargo container in the shape of a rectangular box must have a
volume of 480 cubic feet. If the bottom of the container costs $4
per square foot to construct, and the sides and top of the
container cost $3 per square foot to construct, find the dimensions
of the cheapest container which will have a volume of 480 cubic
feet.

A rectangular box must have a volume of 2 cubic meters. The
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material for the vertical sides costs $ 8 per square meter. (a)
Express the total cost of the box in terms of the length (l) and
width (w) of the base. C = $ (b) Find the dimensions of the box
that costs least. length = meters width = meters height =
meters

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