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Maximize the Volume of a Box: Exploring Optimization Using Calculus

The process of finding the conditions for a function that represents a certain amount of required effort or which represents a certain needed benefit that gives minimum and maximum values is called optimization. Beginning calculus students are often presented with this type of optimization problem:

We want to make a box with a square base and we only have 12 square meters of cardboard to use in construction of the box. If all of the cardboard is used, what is the maximum volume that the box can have?

Man measuring cardboard box

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Artwork Requirements and Tips

Custom Boxes - Artwork Guidelines

  1. Use the best program for the job. We accept InDesign, Quark Xpress and Illustrator files.
  2. Always include all fonts with submitted files. It is imperative that the correct fonts be provided. Do not reverse out type smaller than 6pt. as it may fill in on press.
  3. Always provide all links and supporting images with submitted files. Any image used in creating your document should be saved seperately to the same disk.
  4. Provide quality images and graphics. Vector graphics (images created through anchor points) work best because they can be stretched, bent and resized without losing quality. Submitted photos must be at no less than 300 dpi at full size. Never force an image to 300 DPI, you must always start out with a higher resolution. Submitted bitmap line art images must be at 1200 DPI.
  5. Some papers and coating will crack. Solid, dark colored areas, which bend around corners, can crack as the fiber from the paper protrudes at the point where the paper is bending. This is called checking. If this is a concern, please discuss it with your representative, so that we may use the best materials for your job.
  6. Registration can vary throughout run. There are machine limits associated with the lamination and diecutting processes that we utilize. These can result in variances of up to 3/32” depending on the direction. This can cause borders, artwork along/near creases and edges, and centered logos/images to shift. Please keep this in mind when setting artwork. If you have any questions, please discuss it with your representative.