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 0.08 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 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 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 0.08 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 To minimize the cost of the can: Radius of the can: Height of the can: Minimum cost: cents
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter63: Volumes Of Pyramids And Cones
Section: Chapter Questions
Problem 26A: The container is in the shape of a frustum of a right circular cone. The smaller base area is 426...
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Step 1: Given
VIEWStep 2: Let the variables and determine the cost function
VIEWStep 3: Determine the cost function in terms of r only
VIEWStep 4: Find the critical point that minimizes the production cost
VIEWStep 5: Check the production cost is minimum at the critical point using second derivative test
VIEWStep 6: Determine the radius, height and minimum cost of the can
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