A cylinder shaped can needs to be constructed to hold 300 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 = 27rh Area of the top/bottom: A = Ar To minimize the cost of the can: Radius of the can: Height of the can: cents Minimum cost:
A cylinder shaped can needs to be constructed to hold 300 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 = 27rh Area of the top/bottom: A = Ar To minimize the cost of the can: Radius of the can: Height of the can: cents Minimum cost:
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.4: Linear Programming
Problem 23E
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A cylinder shaped can needs to be constructed to hold 300 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 = ar?h
Area of the sides: A = 27rh
Area of the top/bottom: A = AT
To minimize the cost of the can:
Radius of the can:
Height of the can:
Minimum cost:
cents
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