Question 9 (3 points) The initial simplex tableau (without the horizontal and vertical lines) for a...
The final simplex tableau for the linear programming problem is below. Give the solution to the problem and to its dual. Maximize 6x+ 3y subject to the constraints 5x+ ys 60 3x+ 2y s 50 x20, y20 x 1 0 4 0 10 0 10 1 90 For the primal problem the maximum value of M 11 which is attained for xD yL For the dual problem the minimum value of M is , which is attained for u-L Enter...
9.Write the solution that can be read from the simplex tableau below 15 0 0 6 4 1 0 7 0 14 0 26 -1 0 28 33 0 2 -2 0 9 81 |33 0 -27 8 0 02 x0, x 15, x, 0, s, 0, s, 28, s) 81, z 2 2 15 , 81 15, 82-4, s3 9,z 1 ,220, r3 O x, 3, x 0, x, 0, s, 0, s 4, s,9, z 1 O x,...
This is the initial tableau of a linear programming problem. Solve by the simplex method. S1 S3 X1 1 2 S2 0 1 X2 3 4 2 N OOO 12 4 1 0 1 0 0 0 1 0 0 - 2 - 1 0 The maximum is when X1 = O, x2 =D Sy = 10, s2 = 0, and s3 = 2.
Introduce slack variables as necessary and then write the initial simplex tableau for the given linear programming problem. Complete the initial simplex tableau. 1 1 X, X2 X3 s, 3 8 5 0 2 2 0 0 ONN S2 S3 0 0 0 0 0 0 NOOO 1 12 9 9 1 0 Z= X1 +8X2 +3X3 Maximize subject to X1 8X4 +2x2 +X2 +3x3 12 + 5x3 39 + 2x3 = 9 20, X3 20. 2x X1 20, X2
Introduce slack variables as necessary and then write the initial simplex tableau for the Maximize z = xy + 9x2 given linear programming problem. subject to X1 + 2x2 = 12 8x1 + x2 = 11 5x7 + 2x2 57 with Xq 20, X220 Complete the initial simplex tableau. X1 S1 S2 z X2 2 S3 0 1 1 ol 00 0 0 0 11 O 2 0 7 0 0 0 1 0
The
initial tableau of a linear programming problem is given. Use the
simplex method to solve it.
X1 X2 x3 S1 S2 z 1-0여 8 3 8 1 0 110 -3 -24 1 0 0 0
1) Consider the simplex tableau obtained after a few iterations: RHS Basic 1 1/4 5/8 57/4 57/4 0 01/4 1 1/8 /2 14 3/2 1/4 1/8 5/8 0 a) (10pts) We do not know the original problem, but is given that x and xs are the slack variables for the first and second constraints respectively. The initial basis was constructed as хв=fu xs] and after several simplex tableau iter tions the optimal basis is determined as x [x, x]. From...
3. (2 points) The tableau r421 21 02 5 3 2 10 1 6 4 2 1 0 0 0 represents a solution to the linear programming problem Minimize z 41 22 + r3, subject to the constraints 31 +2a2+r3 6, that satisfies the optimality criterion but is infeasible. Use the dual simplex method to restore feasiblity and hence find an optimal solution.
Q1. (Basic Concept of the Simplex Procedure) (3 marks) This question is about the "Pivoting" step in the Simplex algorithm procedure. The step updates the Simplex tableau by pivoting on the intersection of the entering-variable column and the leaving variable row, i.e. perform EROs on the tableau to get a 1 in the pivot position, and 0s above and below it. We know that one ERO type is "Add a multiple of one row to another row." Consider that we...
Q1. (Basic Concept of the Simplex Procedure) (3 marks) This question is about the "Pivoting" step in the Simplex algorithm procedure. The step updates the Simplex tableau by pivoting on the intersection of the entering-variable column and the leaving variable row, i.e. perform EROs on the tableau to get a 1 in the pivot position, and 0s above and below it. We know that one ERO type is "Add a multiple of one row to another row." Consider that we...