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.

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter59: Areas Of Rectangles, Parallelograms, And Trapezoids
Section: Chapter Questions
Problem 79A
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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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