Question

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

Area of the sides: A=2πrhA=2πrh

Area of the top/bottom: A=πr2A=πr2

To minimize the cost of the package:

radius:

height:

minimum cost:

Answer #1

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 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 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...

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.)

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,...

An open-top rectangular box is being constructed to hold a
volume of 300 in3. The base of the box is made from a
material costing 8 cents/in2. The front of the box must
be decorated, and will cost 12 cents/in2. The remainder
of the sides will cost 2 cents/in2.
Find the dimensions that will minimize the cost of constructing
this box.
Front width: _______ in.
Depth: ________ in.
Height: ________ in.

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