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A rectangular silo with open top and has a square base for food storage is a school project of two senior high school students. They were asked to create to model a storage that will maximize the target volume to be stored. However, they are wondering what would be the maximum dimensions of their silo if it will have a fixed volume of 2.5m3.

A rectangular silo with open top and has a square base for food storage is a school project of two senior high school students. They were asked to create to model a storage that will maximize the target volume to be stored. However, they are wondering what would be the maximum dimensions of their silo if it will have a fixed volume of 2.5m3.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A rectangular silo with open top and has a square base for food storage is a school project of two senior high school students. They were asked to create to model a storage that will maximize the target volume to be stored. However, they are wondering what would be the maximum dimensions of their silo if it will have a fixed volume of 2.5m3. Steps Solution 1. Draw a diagram. List what is asked on the problem and label the diagram with relevant data. Constraint equation: 2. Write the constraint and the optimization equations. Optimization equation: 3. On the constraint equation, solve for y. Then, substitute that equation to its corresponding y on the optimization equation. 4. Simplify and take its first derivative. 5. Set the equation to zero and solve for the x value (critical point). 6. Test the x value. Substitute it to the second derivative and check whether the answer is less than or greater than zero. 7. Substitute the maximum x value to the simplified constraint equation to solve for and y = dimensions of the rectangle. x = are the у.
Transcribed Image Text:A rectangular silo with open top and has a square base for food storage is a school project of two senior high school students. They were asked to create to model a storage that will maximize the target volume to be stored. However, they are wondering what would be the maximum dimensions of their silo if it will have a fixed volume of 2.5m3. Steps Solution 1. Draw a diagram. List what is asked on the problem and label the diagram with relevant data. Constraint equation: 2. Write the constraint and the optimization equations. Optimization equation: 3. On the constraint equation, solve for y. Then, substitute that equation to its corresponding y on the optimization equation. 4. Simplify and take its first derivative. 5. Set the equation to zero and solve for the x value (critical point). 6. Test the x value. Substitute it to the second derivative and check whether the answer is less than or greater than zero. 7. Substitute the maximum x value to the simplified constraint equation to solve for and y = dimensions of the rectangle. x = are the у.
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