A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 450 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.02 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 = Tr²h Area of the sides: A = 2mrh Area of the top/bottom: A πr² = To minimize the cost of the package: Radius: Height: Minimum cost: cm cm cents
A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 450 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.02 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 = Tr²h Area of the sides: A = 2mrh Area of the top/bottom: A πr² = To minimize the cost of the package: Radius: Height: Minimum cost: cm cm cents
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 450 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.02 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: �=��2ℎ
Area of the sides: �=2��ℎ
Area of the top/bottom: �=��2
To minimize the cost of the package:
Radius: (cm)
Height: (cm)
Minimum cost: (cents)
Transcribed Image Text:A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 450 cubic
centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.02 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 = Tr²h
Area of the sides: A = 2πrh
Area of the top/bottom: A = T²
To minimize the cost of the package:
Radius:
Height:
Minimum cost:
cm
cm
cents
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