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Please help me solve this problem. Thanks! Problem 1 (weight 25%) Consider the problem Maximise f(x, y, z) = x + y +2z when g(x,y,z) = x2 +y2 +2z2 = 4. (*) (a) Explain why the problem (*) does have a...
Use Lagrange multipliers to find the min and max of f(x,y,z) = x2-y2+ 2z subject to the constraint x2 + y2 + z2 = 1.
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+y2- 1 1. (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x -0.9y-z 2 x2+ y2- 0.9. Solve the following problem...
Solve the following problem using Lagrange multiplier method: Maximize f(x,y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+ y2- 1 (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above constraints are changed to: (3) (4) 2x-0.9y-z =2 x2+y2- 0.9 Solve the following problem using Lagrange...
please answer step by step Solve the following problem using Lagrange multiplier method: Maximize f(x.y,z) = 4y-2z subject to the constraints 2x-y-z 2 x2+ y2-1 1. (1) (2) (Note: You need not check the Hessian matrix, just find the maximum by evaluating the values of f(x,y,z) at the potential solution points) Also, using sensitivity analysis, find the change in the maximum value of the function, f, if the above changed to: (3) (4) constraints are 2x-0.9y-z 2 x2+y2-0.9. Solve the...
Find the extreme values of the function subject to the given constraint. f(x y, z)=x+2y-2z x2 + y2 + 22-9 Maximum: 9 at(1, 2, -2); minimum: -9 at (-1 -2.2) Maximum: 1 atil -2 -2); minimum: -1 at (-1 2. 2) Maximum: 8 at (2.1, -2): minimum: -8 at (-2-1. 21 Maximum: 1 at (-1-2-3); minimum: -1 at(1.2.3
Problem 1: Consider the following problem x+y+1=1 x2 +y2+z2 =1 max f(x ,y,z)=er+y+1 subject to (a) Solve the problem. (b) Replace the constraints byx+y+1=1.02 and x2+y2+Z2-0.98. What is the approximate change in the optimal value of the objective function? (c) Classify the candidate points for optimality in the local optimization problem.
7a please SM 7. Consider the problem min x? - 2x + 1 + y2 - 2y s.t. (x + y) x +y + b = 2/a where a and b are positive constants and x and y are positive. (a) Suppose that (x, y) solves the problem. Show that x and y must then satisfy the equations x = y and 2r'+br = a The equations in () define x and y as differentiable functions of a and b....
please help me solve the following question 8. Compute JJ f dS where f(x, y, 2)22+2 and S is the top hemisphere x2 + y2 + Z2, 220. 9. Compute JJ F-n dS where F-: (x, y, z) and s is the cone z2 x2 + y2, 0 S 2 1; with the outward pointing normal. 8. Compute JJ f dS where f(x, y, 2)22+2 and S is the top hemisphere x2 + y2 + Z2, 220. 9. Compute JJ...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the boundary of S with counterclockwise orientation when looking down from the z-axis. Verify Stokes' Theorem as follows. (a) (i) Sketch the surface S and the curve C. Indicate the orientation of C (ii) Use the...