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 current value of the objective function?

Is this the last iteration of the simplex method for this problem?

Perform the next iteration of the simplex tableau method. That is, determine the pivot row, pivot column, and the pivot element,and do the necessary row operations (list them to the right of the tableau, beside the row you are changing).

Expert Solution

Colby Messinger answered 2 years ago

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.

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 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

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

Max Z = 6x1 + 10x2+9x3 + 20x4 st 4x1 + 9x2 + 7x3 + 10x4...

Max Z = 6x1 + 10x2+9x3 + 20x4 st 4x1 + 9x2 + 7x3 + 10x4 = 600 x1 + x2 +3x3 + 40x4 = 400 3x1 + 4x2 + 2x3 + x4 = 500 x1,x2,x3,x4 ≥ 0 Which variables are basic in the optimal solution? Explain.

Consider the following integer linear programming problem: Max Z = 4.2x + 4.8y + 5.6z Subject...

Consider the following integer linear programming problem: Max Z = 4.2x + 4.8y + 5.6z Subject to: 4x + 2y + 7z ≤ 37 4x + 4y + 5z ≤ 40 2.8y ≤ 10 x, y, z ≥ 0 and integer What is the optimal solution to the integer linear programming problem? State the optimal values of decision variables.

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

consider the linear programming problem maximize z = x1 +x2 subjected tp x1 + 3x2 >=...

consider the linear programming problem maximize z = x1 +x2 subjected tp x1 + 3x2 >= 15 2x1 + x2 >= 10 x1 + 2x2 <=40 3x1 + x2 <= 60 x1 >= 0, x2>= 0 solve using the revised simplex method and comment on any special charateristics of the optimal soultion. sketch the feasible region for the problem as stated above and show on the figure the solutions at the various iterations

Consider the following linear programming problem Maximize 6x1 + 4x2 + 5x3 Subject to: 2x1 +...

Consider the following linear programming problem Maximize 6x1 + 4x2 + 5x3 Subject to: 2x1 + 3x2 + x3 ≥ 30 2x1 + x2 + x3 ≤ 50 4x1 + 2x2 + 3x3 ≤ 120 x1, x2, x3 ≥ 0 a) Find the optimal solution by using simplex method b) Find the dual price for the first constraint. c) Find the dual price for the second constraint. d) Find the dual price for the third constraint. e) Suppose the right-hand...

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...

Question