Question

Denali Dumpsters need to manufacture a dumpster with an open top and a total volume of 350 cubic feet. The material for the bottom costs $1.25 per square foot and the material for the sides cost $0.75 per square foot.

a) What dimensions will minimize the cost?

b.) What is the minimum cost?

Answer #1

A company plans to manufacture a rectangular box with a square
base, an open top, and a volume of 404 cm3. The cost of the
material for the base is 0.5 cents per square centimeter, and the
cost of the material for the sides is 0.1 cents per square
centimeter. Determine the dimensions of the box that will minimize
the cost of manufacturing it. What is the minimum cost?

ASAP
A company plans to manufacture a rectangular container with a
square base, an open top, and a volume of 320 cm3. The cost of the
material for the base is 0.8 cents per square centimeter, and the
cost of the material for the sides is 0.2 cents per square
centimeter. Determine the dimensions of the container that will
minimize the cost of manufacturing it. What is the minimum
cost?

We must build a crate with square top and bottom whose volume is
8000 cubic inches. The material for the top and the bottom costs
$0.09 per square inch; the material for the sides costs $0.05 per
square inch. What (exact) dimensions minimize the total cost? What
is the total cost (to the nearest cent)?

An open-top box has a square bottom and is made to have a volume
of 50in^3. The material for the base costs $10 a sq in and the
material for the sides is $6 a sq in.
What dimensions minimize cost

We are tasked with constructing a rectangular box with a volume
of 14 cubic feet. The material for the top costs 8 dollars per
square foot, the material for the 4 sides costs 2 dollars per
square foot, and the material for the bottom costs 7 dollars per
square foot. To the nearest cent, what is the minimum cost for such
a box?

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=?

A storage company must design a large rectangular container with
a square base. The volume is 24576ft324576ft3. The material for
the top costs $12$12 per square foot, the material for the sides
costs $2$2 per square foot, and the material for the bottom costs
$12$12 per square foot. Find the dimensions of the container that
will minimize the total cost of material.

A rectangular box is to have a square base and a volume of 48
ft3. If the material for the base costs 4 cents per square foot,
material for the top costs 20 cents per square foot, and the
material for the sides costs 16 cents per square foot, determine
the dimensions of the square base (in feet) that minimize the total
cost of materials used in constructing the rectangular box.

A rectangular box is to have a square base and a volume of 45
ft3. If the material for the base costs 14 cents per square foot,
material for the top costs 6 cents per square foot, and the
material for the sides costs 6 cents per square foot, determine the
dimensions of the square base (in feet) that minimize the total
cost of materials used in constructing the rectangular box.

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.

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