SOLVE STEP BY STEP, SOLVE WITHOUT ARTIFICIAL INTELLIGENCE, BY HAND, LEGIBLE Lagrange multipliers for solving optimization problems with constraints. f(x, y, z) = xyz; x² + 2y² + 3z² = 6 A rectangular box has volume V=xyz, find the values of its sides subject to the constraint x + y + z = 1 , such that V is maximum.

Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x+y+z=26. Find the minimum value of f(x,y)=61x2+6y² subject to the constraint x²+y²=4

Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = xy subject to the constraint that 4x² + y² = 8.

Find the maximum value of z = 4x + 5y, subject to the following constraints: y ≥ 0; x+y≤5; 2x+y≤6; x ≥ 0 For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BIUS Paragraph Arial - P ABC ¶"" Ω Θ 8 x 10pt H :3 出用 EXE A 图 ^

Use the method of Lagrange multipliers to find the maximum/minimum values of the function ?(?, ?, ?) = 2? + 2? + ? subject to the constraint ?^2+y^2+z^2=9 . (Note that f is a function of three variables.)

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Minimize: subject to: z = x - y 4x - 3y 20 3x - 4y ≤ 0 x, y ≥ 0

Find the maximum values of subject to the constraint (Use the Lagrange Multiplier) f(x, y) = 81x? + y? 4x² + y² = 1 Please choose one: a.2nd b.81/4 C.one D.0 to.81/2

Please give a clear and detailed solution. Use Lagrange multipliers to find the maximum and minimum values of this function subject to the constraint.

A satellite television reception station is to be located at point P so that the sum of the squares of the distances from P to the three towns A, B, and C is a minimum. Town A is located at (0,0), town B is located at (2,9), and town C is located at (10,0). Find the coordinates (x.y) of point P, that will minimize the cost of providing B(2,9) 8- 4- satellite cable television for all three towns. A(d.0) 6 (10,0) 12 The station should be placed at the point (Type an ordered pair.)