I'm really stuck on this applied project question from Stewart Calculus, 7th edition. I need help solving questions 4 and 5.

avatar_roku01

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I pasted my current thinking of how I may approach questions 4 and 5 below. I understand Lagrange multipliers well, but I am still pretty lost in solving these 2 questions since its so math heavy, and I am not really sure how to approach them. I understand that this is a lengthy problem, so I am mainly trying to focus on questions 4 and 5 which I believe is the main bulk of the applied project. My apologies for the strange formatting.

Applied Project: Rocket Science- https://www.stewartcalculus.com/data/ESSENTIAL CALCULUS Early Transcendentals/upfiles/projects/ess_wp_1108a_stu.pdf

My current thinking:

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I also tried expanding the function below, as question 3 hints that I need to expand it using log properties, but I am unsure of what to do after.

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