MediumLagrange multipliers

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.7 Constraints and Lagrange Multipliers, #20 · Multivariable Calculus · Lagrange multipliers

(a) Find by Lagrange multipliers the volume … of the largest box…

(a) Find by Lagrange multipliers the volume $V = x y z$ of the largest box with sides adding up to $x + y + z = k$ . (b) Check that $λ = d V_{m a x} / d k$ . (c) United Airlines accepts baggage with $x + y + z = 10 8^{''}$ . If it changes to $11 1^{''}$ , approximately how much (by $λ$ ) and exactly how much does $V_{m a x}$ increase?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.7 Constraints and Lagrange Multipliers, #20

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