Consider the linear equations 2.99x+ 3.00y -4.00 3.00x + 2.99y -4.00 a] Check geometrically and computationally...

 

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Consider the linear equations 2.99x+ 3.00y -4.00 3.00x + 2.99y -4.00 a] Check geometrically and computationally whether the system is ill-conditioned or not. b] Write Jacobi and Gauss-Seidel iterative algorithms to solve the above system o linear equations (b) Consider the following linear program: Objective: Maximize 10x + 5x + 4x3 + 8x4 Subject to: 2x1 + x2 X3 +2x4 X1, 2, X3, X4 20 Work through the simplex algorithm step by step to find all of the optimal solutions. (c) Consider the following linear program: Objective: Maximize 2x Subject to: X1 2x1 + 4x + 3x3 2x + + 4x + X3 X3 X1, X2, X3 > 2x1 2x Objective: Maximize 3x + 2x + Subject to: 3x1 x2 X 3x + = < 6 4 Work through the simplex algorithm step by step to find the optimal solution. Show the steps of the simple algorithm. (d) Consider the following linear program: 4x3 X3 X3 > X3 Z X1, 2, X3 > 20 50 0 -6 3 4 0 Work through the simplex algorithm step by step to show that there are no feasible solution to this linear program. Consider the linear equations 2.99x+ 3.00y -4.00 3.00x + 2.99y -4.00 a] Check geometrically and computationally whether the system is ill-conditioned or not. b] Write Jacobi and Gauss-Seidel iterative algorithms to solve the above system o linear equations (b) Consider the following linear program: Objective: Maximize 10x + 5x + 4x3 + 8x4 Subject to: 2x1 + x2 X3 +2x4 X1, 2, X3, X4 20 Work through the simplex algorithm step by step to find all of the optimal solutions. (c) Consider the following linear program: Objective: Maximize 2x Subject to: X1 2x1 + 4x + 3x3 2x + + 4x + X3 X3 X1, X2, X3 > 2x1 2x Objective: Maximize 3x + 2x + Subject to: 3x1 x2 X 3x + = < 6 4 Work through the simplex algorithm step by step to find the optimal solution. Show the steps of the simple algorithm. (d) Consider the following linear program: 4x3 X3 X3 > X3 Z X1, 2, X3 > 20 50 0 -6 3 4 0 Work through the simplex algorithm step by step to show that there are no feasible solution to this linear program.