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- 1. Solve using Gauss Jordan Elimination Method. Compute also for x, y and z.Solve max f( x,y , z) 3x2+y problem by means of Lagrange multipliers under the constraints of 4x-3y=9 and x2+z2=9. Explain what the values of Lagrange multipliers mean?A function, z = ax + by, is to be optimized subject to the constraint, x2 + y2=1 where a and b are positive constants. Use Lagrange multipliers to show that this problem has only one solution in the positive quadrant (i.e. in the region x > 0, y > 0) and that the optimal value of z is √a2 +b2.
- This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, y, z) = 4x + 4y + 7z, 2x2 + 2y2 + 7z2 = 23Suppose that a temperature of a metal plate is given by T(x,y)=x2+2x+y2, for points (x,y) on the elliptic plate defined by 6x2+5y2≤60. Find the maximum and minimum temperatures on the plate. Use Lagrange Multipliers to determine the absolute extrema of f on the indicated constraint.Can you show the step by step process of the first order conditions in order to get equation 8.9 , 8.10 and 8.11 Lagrange multipliers. L = Lagrangian Lagrange multipliers: Gamma and Lambda w_p = Portfolio weight
- Consider the problem (attached image) min x2 subject to x2 = 1 x1, x2 ≥ 0 Write down its dual. For both the primal and the dual problem determine whether they have unique optimal solutions and whether they have nondegeneration optimal solutions.Construct the dual problem associated with the primal problem. Solve the primal problem. Minimize C = 30x + 12y + 20z subject to 2x + 4y + 3z ≥ 6 6x + z ≥ 2 6y + 2z ≥ 4 x ≥ 0, y ≥ 0, z ≥ 0Suppose following simplex table: 2 3 1 -1 0 0 -100 x1 x2 x3 x4 x5 x6 x7 b x5 0 7/2 0 0 3/2 1 1/2 -3/2 14 x3 1 5/2 0 1 1/2 0 1/2 1/2 13 x2 3 0 1 0 1 0 0 1 17 Z - C We can say, that: Select one: The solution is not optimal. The solution is optimal. The solution can be the initial solution.
- Consider the following linear program : z = 6x1 + 6x2 + 10x3 → min s.t. 4x1 + 3x2 + 2x3 ≥ 16 x1 + 2x2 + 5x3 ≥ 16 x1, x2, x3 ≥ 0 a) 1. Build the dual problem corresponding to the given problem! b) Solve the dual problem graphically! Determine the exact coordinates by computing the intersection point of two appropriate lines! c) Conclude for the solution (objective and variables) of the primal problem by using the complementary slackness conditions.1. a. Show that this model has an unbounded solution by Big M Method. b. What can be changed to have a bounded solution for this model? Explain by solving it. Max Z= 3x1 + 6x2 s.to 3x1 + 4x2 ≥ 12 -2x1+ x2 ≤ 4 x1, x2 ≥ 02. Use the standard simplex method to solve using your first pivot choice. Provide the sequence of points given in the tableau. Maximize: P=5x+4y Subject to: 2x+y<=80 2x+3y<=120 4x+y<=160 x>=0,y>=0