#5. A rectangular box with no lid will be made of cardboard and have a surface area of 24 square feet.Find the dimensions that will have the maximum possible volume. Use Lagrange multipliers.nt#6. Consider the point P(5, -8, 0) and the sphere x² + y² + z² = 9. Find the point on the sphere that isclosest to the point P and the point on the sphere that is the farthest from the point P.

The rectangular box with no lead has a surface area of Note: According to the guidelines we are…

Answered: #5. A rectangular box with no lid will…

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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I will accept a package whose combined height and perimeter of the base are at most 140 inches. Use Lagrange multipliers to find the dimensions of the largest volume box that will be accepted.
Rain is designing a new bottle for Luscious Curls shampoo. The bottle should have a volume of 450 cm³. The company they work for wants to minimize the amount of plastic used per bottle, however the company would like to have a choice between two B3 of three shapes; a cylinder, triangular prism, or rectangular prism. Help Rain to determine the most efficient dimensions of the two most efficient shapes for the bottle with the minimum surface area.Also calculate the surface area of the shapes. Show your work. Bottle choice 1 Bottle choice 2 Bottle choice 1 Bottle choice 2 show your work here Shape and dimensions Shape and surface area
You are designing a glass candle holder. It will be a rectangular prism with outer surface area 200 m2, a square base, and no top. Determine the dimensions with the maximum volume of the candle holder.

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#5. A rectangular box with no lid will be made of cardboard and have a surface area of 24 square feet. Find the dimensions that will have the maximum possible volume. Use Lagrange multipliers.