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1) The Betty Moore Company requires that its beef stew containers have a capacity of 64 in3., have the shape of right circular cylinders, and be made of aluminum. Determine the radius and height of the container the requires the least amount of metal.

1) The Betty Moore Company requires that its beef stew containers have a capacity of 64 in3., have the shape of right circular cylinders, and be made of aluminum. Determine the radius and height of the container the requires the least amount of metal.

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 37CR
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Answer each of these optimization questions. Identify what is to be optimized, what is the constraint,
and show all necessary work in solving these questions. 

Answer each of these optimization questions. Identify what is to be optimized, what is the constraint, and show all necessary work in solving these questions. 1) The Betty Moore Company requires that its beef stew containers have a capacity of 64 in3., have the shape of right circular cylinders, and be made of aluminum. Determine the radius and height of the container the requires the least amount of metal. 2) An open box constructed from a tin sheet has a square base and a volume of 216 in cubed. Find the dimensions of the box, assuming that the minimum amount of material was used in its construction. 3) An apple orchard has an average yield of 36 bushels of apples per tree if the tree density is 22 trees per acre. For each unit increase in tree density, the yield decreases by 2 bushels per tree. How many trees per acre should be planted to maximize the yield?
Transcribed Image Text:Answer each of these optimization questions. Identify what is to be optimized, what is the constraint, and show all necessary work in solving these questions. 1) The Betty Moore Company requires that its beef stew containers have a capacity of 64 in3., have the shape of right circular cylinders, and be made of aluminum. Determine the radius and height of the container the requires the least amount of metal. 2) An open box constructed from a tin sheet has a square base and a volume of 216 in cubed. Find the dimensions of the box, assuming that the minimum amount of material was used in its construction. 3) An apple orchard has an average yield of 36 bushels of apples per tree if the tree density is 22 trees per acre. For each unit increase in tree density, the yield decreases by 2 bushels per tree. How many trees per acre should be planted to maximize the yield?
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