A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 400 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.04 cents per square centimeter. The top will be made of glued paper, costing 0.08 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 = ²h Area of the sides: A = 2πrh Area of the top/bottom: A = ² To minimize the cost of the package: Radius: 6.5144 Height: Minimum cost: X cm cm cents
A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 400 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.04 cents per square centimeter. The top will be made of glued paper, costing 0.08 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 = ²h Area of the sides: A = 2πrh Area of the top/bottom: A = ² To minimize the cost of the package: Radius: 6.5144 Height: Minimum cost: X cm cm 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 microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 400 cubic
centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.04 cents per
square centimeter. The top will be made of glued paper, costing 0.08 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 = Tr²h
Area of the sides: A = 2πrh
Area of the top/bottom: A = ²
To minimize the cost of the package:
Radius: 6.5144
Height:
Minimum cost:
X
cm
cm
cents
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