Please help to find the dimension that will maximize ?

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SUMMARY

The discussion centers on optimizing the dimensions of a shelter for hikers along the Appalachian Trail, specifically to maximize volume while using 384 square feet of wood. The shelter design includes a back, a top, and two sides. Participants emphasize the importance of providing initial attempts or calculations to facilitate assistance. The problem requires applying principles of optimization and geometry to determine the ideal length, width, and height of the shelter.

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  • Understanding of optimization techniques in calculus
  • Familiarity with geometric volume calculations
  • Knowledge of constraints in mathematical problems
  • Basic skills in algebra for solving equations
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  • Study optimization problems using calculus, focusing on volume maximization
  • Learn about geometric properties of rectangular prisms
  • Explore methods for setting up and solving constrained optimization problems
  • Review examples of real-world applications of optimization in construction
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This discussion is beneficial for mathematicians, engineers, architects, and anyone involved in designing structures that require efficient use of materials while maximizing space.

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Please help to find the dimension that will maximize...?

The Park Service is building shelters for hikers along the Appalachian Trail. Each shelter has a back, a top, and two sides. Find the dimensions that will maximize the volume while using 384 square feet of wood.

length (across the front) =... feet
width (from front to back) = ....feet
height (ground to top) =..... feet
λ=.....

volume = .....ft3

any help appreciated
 
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peace89 said:
The Park Service is building shelters for hikers along the Appalachian Trail. Each shelter has a back, a top, and two sides. Find the dimensions that will maximize the volume while using 384 square feet of wood.

length (across the front) =... feet
width (from front to back) = ....feet
height (ground to top) =..... feet
λ=.....

volume = .....ft3

any help appreciated

What have you tried to do? We can't and won't help you if you haven't shown an attempt.
 

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