Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.7 Constraints and Lagrange Multipliers, #29 · Multivariable Calculus · Lagrange multipliers

Minimize … subject to the inequality constraint

These problems allow inequality constraints, optional but good.

Minimize $f = x^{2} + y^{2}$ subject to the inequality constraint $x + y \leq 4$ . The minimum is obviously at ______, where $f_{x}$ and $f_{y}$ are zero. The multiplier is $λ =$ ______. A small change from 4 will leave $f_{m i n} =$ ______ so the sensitivity $d f_{m i n} / d k$ still equals $λ$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.7 Constraints and Lagrange Multipliers, #29

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