Solve the following linear programming problem using generalised simplex method Maximise z= 2x1+3x2 subject to -2x1+x2>=3...

Solve the following linear programming problem using generalised simplex method

Maximise z= 2x1+3x2

subject to -2x1+x2>=3

3x1+x2<=5

x1,x2>=0

Expert Solution

milcah answered 2 years ago

Simplex Method Consider the following linear programming problem: max z = 6x1 + 3x2 - 9x2...

Simplex Method Consider the following linear programming problem: max z = 6x1 + 3x2 - 9x2 - 9x3 + 15x4 s.t. 2x1 + 4x2 +6x3 + 8x4 <= 80 6x1 - 3x2 +3x3 + 6x4 <= 24 12x1 - 6x2 + 3x3 - 3x4 <= 30 x1, x2, x3, x4 >= 0 Rewrite the problem in standard form, that is, add the necessary slack variables in order to consider only equality constraints (and non-negativity). What is the...

For the following linear programming problem: Maximize z = 2x1+ x2 Such that ...

For the following linear programming problem: Maximize z = 2x1+ x2 Such that x1+ 2x2 ≤ 12 x2 ≥ 3 x1,x2 ≥ 0 (a) Write the first two constraints in equation form by adding slack or subtracting excess (surplus) variables. (b)Find all basic solutions for this LP (c) Which of these solutions are feasible? (d)Which of these feasible solutions is optimal? Find the optimal value of z

Solve the following linear programming problem using the dual simplex method: max ? = −?1 −...

Solve the following linear programming problem using the dual simplex method: max ? = −?1 − 2?2 s.t. −2?1 + 7?2 ≤ 6 −3?1 + ?2 ≤ −1 9?1 − 4?2 ≤ 6 ?1 − ?2 ≤ 1 7?1 − 3?2 ≤ 6 −5?1 + 2?2 ≤ −3 ?1,?2 ≥ 0

Consider the following linear programming problem: Max Z = 3x1 + 3x2 Subject to: ...

Consider the following linear programming problem: Max Z = 3x1 + 3x2 Subject to: 10x1 + 4x2 ≤ 60 25x1 + 50x2 ≤ 200 x1, x2 ≥ 0 Find the optimal profit and the values of x1 and x2 at the optimal solution.

Maximization by the simplex method Solve the following linear programming problems using the simplex method. 1>....

Maximization by the simplex method Solve the following linear programming problems using the simplex method. 1>. Maximize z = x1 + 2x2 + 3x3 subject to x1 + x2 + x3 ≤ 12 2x1 + x2 + 3x3 ≤ 18 x1, x2, x3 ≥ 0 2>. A farmer has 100 acres of land on which she plans to grow wheat and corn. Each acre of wheat requires 4 hours of labor and $20 of capital, and each acre of corn...

Use the Simplex method to solve the following LP minimize −2x1 −3x2 + x3 + 12x4...

Use the Simplex method to solve the following LP minimize −2x1 −3x2 + x3 + 12x4 subject to −2x1 −9x2 + x3+ 9x4 + x5 = 0 1/3x1 + x2 −1/3x3 −2x4 + x6 = 0 x1,x2,x3,x4,x5,x6 ≥ 0

Solve this problem with the revised simplex method: Maximize Z = 5X1 + 3X2 + 2X3...

Solve this problem with the revised simplex method: Maximize Z = 5X1 + 3X2 + 2X3 Subject to 4X1 + 5X2 + 2X3 + X4 ≤ 20 3X1 + 4X2 - X3 + X4 ≤ 30 X1, X2, X3, X4 ≥ 0

Use the simplex method to solve the linear programming problem. Maximize objective function: Z= 6x1 +...

Use the simplex method to solve the linear programming problem. Maximize objective function: Z= 6x1 + 2x2 Subject to constraints: 3x1 + 2x2 <=9 x1 + 3x2 <= 5 when x1, x2 >=0

Solve the following linear programming model graphically: Max Z= 3x1 +4x2 Subject to: 2x1 + 4x2...

Solve the following linear programming model graphically: Max Z= 3x1 +4x2 Subject to: 2x1 + 4x2 <= 22 -x1 + 4x2 <= 10 4x1 – 2x2 <= 14 x1 – 3x2 <= 1 x1, x2, >=0 Clearly identify the feasible region, YOUR iso-profit line and the optimal solution (that is, d.v. values and O.F. Value.

Solve the given linear programming problem using the simplex method. If no optimal solution exists, indicate...

Solve the given linear programming problem using the simplex method. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY if the feasible region is empty and UNBOUNDED if the objective function is unbounded.) Minimize c = x + y + z + w subject to x + y ≥ 80 x + z ≥ 60 x + y − w ≤ 50 y + z − w ≤ 50...

Question