A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 300 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 0.06 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 = r²h Area of the sides: A 2rrh %3D Area of the top/bottom: A = ar2 To minimize the cost of the package: Radius: cm Height: cm Minimum cost: 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 300
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 0.06 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 = ar²h
Area of the sides: A = 2rrh
Area of the top/bottom: A = Tr2
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 300 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 0.06 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 = ar²h Area of the sides: A = 2rrh Area of the top/bottom: A = Tr2 To minimize the cost of the package: Radius: cm Height: cm Minimum cost: cents
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