Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.6 Maxima, Minima, and Saddle Points, #18 · Multivariable Calculus · Gradient & optimization

A box has a corner at … and all edges parallel to…

A box has a corner at $(0, 0, 0)$ and all edges parallel to the axes. If the opposite corner $(x, y, z)$ is on the plane $3 x + 2 y + z = 1$ , what position gives maximum volume? Show first that the problem maximizes $x y - 3 x^{2} y - 2 x y^{2}$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.6 Maxima, Minima, and Saddle Points, #18

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