Optimization minimize the amount of material used.

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SUMMARY

The discussion focuses on optimizing the dimensions of a box with a square base and an open top to minimize the material used while maintaining a volume of 62,500 cm³. Participants recommend starting by defining variables for the height and side length of the base, followed by formulating equations for both volume and surface area. The key steps involve sketching the problem, identifying constraints, and applying calculus to find the optimal dimensions. This structured approach simplifies the process of solving optimization problems in mathematics.

PREREQUISITES
  • Understanding of basic calculus principles
  • Familiarity with optimization techniques
  • Ability to formulate equations based on geometric constraints
  • Knowledge of volume and surface area calculations for geometric shapes
NEXT STEPS
  • Study calculus applications in optimization problems
  • Learn how to derive equations for volume and surface area of geometric shapes
  • Explore techniques for sketching and visualizing mathematical problems
  • Practice solving similar optimization problems involving different geometric configurations
USEFUL FOR

Students, educators, and professionals in mathematics or engineering fields who are interested in mastering optimization techniques and applying calculus to real-world problems.

calcula
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Hi
I am having a lot of trouble with this problem. I don't actually know where to begin.

A box with a square base and open top must have a volume of 62,500 cm3. Find the dimensions of the box that minimize the amount of material used.

Need to find:
sides of base cm
height cm

Thanks
 
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calcula said:
Hi
I am having a lot of trouble with this problem. I don't actually know where to begin.

A box with a square base and open top must have a volume of 62,500 cm3. Find the dimensions of the box that minimize the amount of material used.

Need to find:
sides of base cm
height cm

Thanks

The usual place to start is to name your variables, say the height of the box and the length of the sides. Then can you write formulas for the volume of the box and area of materials used in terms of those variables?
 
Oh boy, I remember when I started doing maths that I had problems trying to turn words into maths

What I did was sketched the problem out along with all variables and what they represent.
Then write down your equations, how do I find volume? what restrictions does the statement 'square base and open top' place on the variables? what will give me the amount of material used?

Once you've got everything written down, then you start with your calculus

If you're anything like me, once you've got this down correctly you'll end up loving doing those elementary optimization problems!
 

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