A cylinder shaped can needs to be constructed to hold 550 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 0.06 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 = ²h Area of the sides: A = 2πrh Area of the top/bottom: A = πr² To minimize the cost of the can: Radius of the can: Height of the can: Minimum cost: cents

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question 36
A cylinder shaped can needs to be constructed to hold 550 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 0.06 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 = är²h
Area of the sides: A = 2πrh
Area of the top/bottom: A = T²
To minimize the cost of the can:
Radius of the can:
Height of the can:
Minimum cost:
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Transcribed Image Text:Question 36 A cylinder shaped can needs to be constructed to hold 550 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 0.06 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 = är²h Area of the sides: A = 2πrh Area of the top/bottom: A = T² To minimize the cost of the can: Radius of the can: Height of the can: Minimum cost: Question Help: Video > Submit Question cents
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