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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.2 Maximum and Minimum Problems, #23 · Calculus · Optimization

The airlines accept a box if length + width + height …

The airlines accept a box if length + width + height $= 1 + w + h \leq 6 2^{''}$ or $158 cm$ . If $h$ is fixed show that the maximum volume $(62 - w - h) w h$ is $V = h (31 - \frac{1}{2} h)^{2}$ . Choose $h$ to maximize $V$ . The box with greatest volume is a ____.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.2 Maximum and Minimum Problems, #23

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