Question: BONUS PROBLEM -4.8.5- LaGrange Multipliers Use Lagrange Multipliers for three-variable functions to solve the following problem. Show all processes necessary. If only an answer is

BONUS PROBLEM -4.8.5- LaGrange Multipliers Use Lagrange Multipliers for three-variable functions to solve the following problem. Show all processes necessary. If only an answer is provided, you will receive no credit. ENGINEERING 301- BUILD A BOX - A PAIRED EXERCISE Work with ONE partner or by yourself. Objective: First illustrate an open-top box, then find its dimensions which will create a MAXIMUM volume. Use as many constraints as you feel necessary. You are charged with creating a three-dimensional box with no top that has maximum volume from a 16"$\times 24$" piece of cardboard: 1. Your final answer should have dimensions, in inches, for each side ($ L, W, H $) and the correct maximum volume should be in cubic inches. 2. You must illustrate the box and show all calculations and all equations used. PLEASE SOLVE IN FULL

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