Main

A piece of cardboard with a total area of 0.8m'^2^' is to be made into an open-top box by first removing the corners and then by folding the box sides up and securing the tabs to the adjacent box side. The starting cardboard sheet has height ''h'' and width ''w''. When cut and folded, the box has a width of ''w-2x'', a length of ''h-2x'', and a height of ''x''. In order to properly secure the tabs to the adjacent box side, the width of the tab must be 5 centimeters (0.05m). The objective is to maximize the volume of the box by choosing an appropriate value of ''x'' (the height of the box) and ''w'' (the starting width of the cardboard sheet).

* [[Attach:box_folding_problem.pdf | Box Folding Problem]]

* [[Attach:box_folding_solution.pdf | Box Folding Solution]]

## Box Folding Optimization

## Main.BoxFolding History

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A piece of cardboard with a total area of 0.8m'^2^' is to be made into an open-top box by first removing the corners and then by folding the box sides up and securing the tabs to the adjacent box side. The starting cardboard sheet has height ''h'' and width ''w''. When cut and folded, the box has a width of ''w-2x'', a length of ''h-2x'', and a height of ''x''. In order to properly secure the tabs to the adjacent box side, the width of the tab must be 5 centimeters (0.05m). The objective is to maximize the volume of the box by choosing an appropriate value of ''x'' (the height of the box) and ''w'' (the starting width of the cardboard sheet).

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A piece of cardboard with a total area of 0.8m'^2^' is to be made into an open-top box by first removing the corners and then by folding the box sides up and securing the tabs to the adjacent box side. The starting cardboard sheet has height ''h'' and width ''w''. When cut and folded, the box has a width of ''w-2x'', a length of ''h-2x'', and a height of ''x''. In order to properly secure the tabs to the adjacent box side, the width of the tab must be 5 centimeters (0.05m). The objective is to maximize the volume of the box by choosing an appropriate value of ''x'' (the height of the box) and ''w'' (the starting width of the cardboard sheet).

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* [[Attach:box_folding_problem.pdf | Box Folding Problem]]

* [[Attach:box_folding_solution.pdf | Box Folding Solution]]

* [[Attach:box_folding_solution.pdf | Box Folding Solution]]

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* [[Attach:box_folding_problem.pdf | Box Folding Problem]]

* [[Attach:box_folding_solution.pdf | Box Folding Solution]]

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[[Attach:box_folding_problem.pdf | Box Folding Problem]]

[[Attach:box_folding_solution.pdf | Box Folding Solution]]

[[Attach:box_folding_solution.pdf | Box Folding Solution]]

to:

* [[Attach:box_folding_problem.pdf | Box Folding Problem]]

* [[Attach:box_folding_solution.pdf | Box Folding Solution]]

* [[Attach:box_folding_solution.pdf | Box Folding Solution]]

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(:title Box Folding Optimization:)

(:keywords box folding, project, nonlinear, optimization, engineering optimization, engineering design, interior point, active set, circle packing, packing optimization, python, matlab:)

(:description An optimization application to determine the maximum size of a box from a 0.8m^2 piece of cardboard.:)

!!!! Box Folding Optimization

A piece of cardboard with a total area of 0.8m'^2^' is to be made into an open-top box by first removing the corners and then by folding the box sides up and securing the tabs to the adjacent box side. The starting cardboard sheet has height ''h'' and width ''w''. When cut and folded, the box has a width of ''w-2x'', a length of ''h-2x'', and a height of ''x''. In order to properly secure the tabs to the adjacent box side, the width of the tab must be 5 centimeters (0.05m). The objective is to maximize the volume of the box by choosing an appropriate value of ''x'' (the height of the box) and ''w'' (the starting width of the cardboard sheet).

Attach:box_folding.png

[[Attach:box_folding_problem.pdf | Box Folding Problem]]

[[Attach:box_folding_solution.pdf | Box Folding Solution]]

----

!!!! Download Sample Python Code

Python source code solves the box optimization problem with Newton's method, a quasi-Newton's method (BFGS), a steepest descent approach, and a conjugate gradient method. After the script executes, a figure appears that shows a contour plot of the solution with a graphical depiction of the progress of each method.

* [[Attach:Box_Folding_files.zip|Python Example Source Code]]

[[Attach:Box_Folding_files.zip|Attach:Box_Folding_files.png]]

Attach:box_folding_contour.png

----

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(:keywords box folding, project, nonlinear, optimization, engineering optimization, engineering design, interior point, active set, circle packing, packing optimization, python, matlab:)

(:description An optimization application to determine the maximum size of a box from a 0.8m^2 piece of cardboard.:)

!!!! Box Folding Optimization

A piece of cardboard with a total area of 0.8m'^2^' is to be made into an open-top box by first removing the corners and then by folding the box sides up and securing the tabs to the adjacent box side. The starting cardboard sheet has height ''h'' and width ''w''. When cut and folded, the box has a width of ''w-2x'', a length of ''h-2x'', and a height of ''x''. In order to properly secure the tabs to the adjacent box side, the width of the tab must be 5 centimeters (0.05m). The objective is to maximize the volume of the box by choosing an appropriate value of ''x'' (the height of the box) and ''w'' (the starting width of the cardboard sheet).

Attach:box_folding.png

[[Attach:box_folding_problem.pdf | Box Folding Problem]]

[[Attach:box_folding_solution.pdf | Box Folding Solution]]

----

!!!! Download Sample Python Code

Python source code solves the box optimization problem with Newton's method, a quasi-Newton's method (BFGS), a steepest descent approach, and a conjugate gradient method. After the script executes, a figure appears that shows a contour plot of the solution with a graphical depiction of the progress of each method.

* [[Attach:Box_Folding_files.zip|Python Example Source Code]]

[[Attach:Box_Folding_files.zip|Attach:Box_Folding_files.png]]

Attach:box_folding_contour.png

----

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