fmax = 270, fmin = 0 fmax = 30, fmin = - 30 fmax = 270, fmin = - 270 Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f (x, y) = {image} , {image} fmax = 270, fmin = 0 fmax = 30, fmin = - 30 fmax = 270, fmin = - 270 fmax = 0, fmin = - 30 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

f (x, y, z) = {image} f (x, y, z) = 0.6 f (x, y, z) = 0.7 1. 2. 3. 4. Use Lagrange multipliers to find the maximum value of the function subject to the given constraint. f (x, y, z) = {image} , {image} = 1. f (x, y, z) = {image} f (x, y, z) = 0.6 f (x, y, z) = 0.7 1. 2. 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. Then select the correct answer below. f (x, y, z) = 6 x - y - 9 z; x + 3 y - z = 0, {image} . 1. {image} 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in plane x + 4 y + 5 z = 60. V = 100 V = 409 V = 80 V = 400 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Find the maximum value of {image} given that x1, x2, Find the maximum value of {image} given that x1, x2, ..., xn are positive numbers and x1 + x2 + ... + xn = c, where c is a constant. Find f for n = 3 and c = 28.5 and select the correct answer below. f = 3 f = 9 f = 9.5 f = 6.5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50