Question

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 the sides: A=2πrh

Area of the top/bottom: A=πr^2

To minimize the cost of the can:

Radius of the can:

Height of the can:

Minimum cost: _____ cents

Answer #1

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...

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
0.04 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 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 a cylinder to hold 550 cubic centimeters of soup. The
sides and bottom of the container will be made of syrofoam 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.

A cylindrical can is to have volume 1500 cubic centimeters.
Determine the radius and the height which will minimize the amount
of material to be used.
Note that the surface area of a closed cylinder is
S=2πrh+2πr2 and the volume of a cylindrical can is
V=πr2h
radius =. cm
height = cm

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.)

You have been asked to design a closed rectangular box that
holds a volume of 25 cubic centimeters while minimizing the cost of
materials, given that the material used for the top and bottom of
the box cost 4 cents per square centimeter, and the material used
for sides cost 9 cents per square centimeter. Find the dimensions
of this box in terms of variables L, W, and H.

A manufacturer makes a cylindrical can with a volume of 500
cubic centimeters. What dimensions (radius and height) will
minimize the material needed to produce each can, that is, minimize
the surface area? Explain and show all steps business calculus.

A company is planning to manufacture cylindrical above-ground
swimming pools. When filled to the top, a pool must hold 100 cubic
feet of water. The material used for the side of a pool costs $3
per square foot and the mate-rial used for the bottom of a pool
costs $2 per square foot.(There is no top.) What is the radius of
the pool which minimizes the manufacturing cost? (Hint: The volume
of a cylinder of height hand radius r isV=πr2h,...

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