Question

Suppose the material for the top and bottom costs b cents per square centimeter and the material for the sides costs 0.1 cents per square centimeter. You want to make a can with a volume of k. What values for the height and radius will minimize the cost? (Your answer will have a k and a b in it.)

Answer #1

A cylinder shaped can needs to be constructed to hold 400 cubic
centimeters of soup. The material for the sides of the can costs
0.04 cents per square centimeter. The material for the top and
bottom of the can need to be thicker, and costs 0.05 cents per
square centimeter. Find the dimensions for the can that will
minimize production cost.
Helpful information:
h : height of can, r : radius of can
Volume of a cylinder: V=πr2^h
Area of...

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?

You need a box with a volume of 1000cm3. The top and
the bottom of the box are square and each cost $.20 per square
centimeter, whereas the sides each cost $.05 per square centimeter.
What are the dimensions of the box that will minimize the cost?

A microwaveable cup-of-soup package needs to be constructed in
the shape of cylinder to hold 250 cubic centimeters of soup. The
sides and bottom of the container will be made of styrofoam costing
0.03 cents per square centimeter. The top will be made of glued
paper, costing 0.07 cents per square centimeter. Find the
dimensions for the package that will minimize production
cost.
Helpful information:
h : height of cylinder, r : radius of
cylinder
Volume of a cylinder: V=πr2hV=πr2h...

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

A microwaveable cup-of-soup package needs to be constructed in
the shape of cylinder to hold 550 cubic centimeters of soup. The
sides and bottom of the container will be made of styrofoam costing
0.03 cents per square centimeter. The top will be made of glued
paper, costing 0.07 cents per square centimeter. Find the
dimensions for the package that will minimize production cost.
Helpful information: h : height of cylinder, r : radius of cylinder
Volume of a cylinder: V...

A microwaveable cup-of-soup package needs to be constructed in
the shape of cylinder to hold 350 cubic centimeters of soup. The
sides and bottom of the container will be made of styrofoam costing
0.03 cents per square centimeter. The top will be made of glued
paper, costing 0.06 cents per square centimeter. Find the
dimensions for the package that will minimize production cost.
To minimize the cost of the package:
Radius:
Height:
Minimum cost:

A microwaveable cup-of-soup package needs to be constructed in
the shape of cylinder to hold 350 cubic centimeters of soup. The
sides and bottom of the container will be made of styrofoam costing
0.04 cents per square centimeter. The top will be made of glued
paper, costing 0.08 cents per square centimeter. Find the
dimensions for the package that will minimize production cost:
radius, height, and minimum cost

A box of volume 36 m3 with square bottom and no top
is constructed out of two different materials. The cost of the
bottom is $40/m2 and the cost of the sides is
$30/m2 . Find the dimensions of the box that minimize
total cost. (Let s denote the length of the side of the
square bottom of the box and h denote the height of the
box.)
(s, h) =

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