A cylinder shaped can needs to be constructed to hold 350 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 0.07 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 : πr²h Volume of a cylinder: V = = 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
A cylinder shaped can needs to be constructed to hold 350 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 0.07 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 : πr²h Volume of a cylinder: V = = 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
Problem 1RQ
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A cylinder shaped can needs to be constructed to hold 350 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 0.07 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: �=��2ℎ
Area of the sides: �=2��ℎ
Area of the top/bottom: �=��2
To minimize the cost of the can:
Radius of the can:
Height of the can:
Minimum cost: cents
Transcribed Image Text:A cylinder shaped can needs to be constructed to hold 350 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 0.07 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
Area of the sides: A =
=
πr²h
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
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