Find the minimum value of the objective function z = 6x + 4y, subject to the following constraints. (See Example 3.) 6x + y 2 52 4x + 2y 2 40 2x + 8y 2 48 x 2 0, Υ Σ Ο The minimum value is z = Additional Materials at (x, y) =

Find the minimum and maximum values of the function subject to the given constraint ƒ(x, y) = 12x² +2y², 3x+4y = 1 Enter DNE if such a value does not exist. fmin = fmax =

Find the minimum or maximum value of f (as indicated) subject to the given constraint. Minimum of f(x, y) = x – 14x + y“ – 16y, subject to 2x + 3y = 12 %3D O A. Minimum = - 24 at (2,0) O B. Minimum = - 68 at (1,5) O C. Minimum = -61 at (3,2) O D. Minimum = - 15 at (0,1)

The function f(x,y) = e 1xy has an absolute maximum value and absolute minimum value subject to the constraint x + xy + y = 36. Use Lagrange multipliers to find these values. The absolute maximum is (Type an exact answer in terms of e.)