A cylinder shaped can needs to be constructed to hold 250 cubic centimeters of soup. The material for the sides of the can costs 0.02 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.08 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 = ar²h Area of the sides: A 2rrh Area of the top/bottom: A = r? 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 250 cubic centimeters of soup. The material for the sides of the can costs 0.02 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.08 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 = ar²h Area of the sides: A 2rrh Area of the top/bottom: A = r? To minimize the cost of the can: Radius of the can: Height of the can: Minimum cost: cents
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:A cylinder shaped can needs to be constructed to hold 250 cubic centimeters of soup. The material
for the sides of the can costs 0.02 cents per square centimeter. The material for the top and bottom
of the can need to be thicker, and costs 0.08 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 = ar²h
Area of the sides: A
= 2rrh
Area of the top/bottom: A = Tr2
%3D
To minimize the cost of the can:
Radius of the can:
Height of the can:
Minimum cost:
cents
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