CPS3-solution.p x @ MATH 209 (LEC X 3 Chapter 15.1 - D X @ University of All X Course Hero X Assignment 2 X Assign2 * *Dashboard * + V X eclass.srv.ualberta.ca/pluginfile.php/10395005/mod_resource/content/6/MATH209-Assignment2.pdf *IA : E Assignment 2 5 17 - 128% + Problem 4. The Lagrange multiplier method provides an ingenious approach to tackle optimization prob- lems with constraints, often referred to as conditional maximization. In general, the maximum or minimum of a function f(x, y, z) on a closed surface defined by g(x, y, z)=0 satisfies the tangential condition: Vf ||Vg. Now, apply the Lagrange multiplier method to determine the dimensions of the box that can be inscribed with the maximum volume inside the ellipsoid defined by the equation: 14 C Clear Q Search ENG 8:16 PM US 2023-10-06 1CPS3-solution.p x re MATH 209 (LEC X Chapter 15.1 - D X University of All X Course Hero X Assignment 2 X Assign2 * *Dashboard * + V X eclass.srv.ualberta.ca/pluginfile.php/10395005/mod_resource/content/6/MATH209-Assignment2.pdf *IA : E Assignment 2 7 1 7 - 128% + Problem 6. This problem deals with global minimization and maximization. As we've learned in lectures, a continuous function f(x, y, z) attains its maximum and minimum in any bounded and closed subset of 3. These maximum and minimum points can occur either inside , which, if f is smooth, is captured by the equation Vf=0, or on the boundary bud(). The maximum and minimum of f on bud() can be addressed using the Lagrange multiplier method. Now, determine both the maximum and minimum values of the function f=xy+yz + zx within the region defined by the coordinate planes x=0, y=0, z=0, and the plane cty + z=1, restricted to the first octant. 14 C Q Search ENG 8:16 PM Clear US 2023-10-06 2