MediumLagrange multipliers

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.7 Constraints and Lagrange Multipliers, #25 · Multivariable Calculus · Lagrange multipliers

Figure 13.23 shows the constraint plane … chopped off by the inequalities…

These problems allow inequality constraints, optional but good.

Figure 13.23 shows the constraint plane $g = x + y + z = 1$ chopped off by the inequalities $x \geq 0, y \geq 0, z \geq 0$ . What are the three "endpoints" of this triangle? Find the minimum and maximum of $f = 4 x - 2 y + 5 z$ on the triangle, by testing $f$ at the endpoints.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.7 Constraints and Lagrange Multipliers, #25

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