Question 1

Write the following problem in tableau form. Which variables would be in the initial basis? Max x₁ + 2x₂ s.t. 3x₁ + 4x₂ ≤ 100 2x₁ + 3.5x₂ ≥ 60 2x₁ − 1x₂ = 4 x₁ , x₂ ≥ 0

Accepted Answer

The answer of Write the following problem in tableau form....

Question 2

Infeasibility exists when one or more of the artificial variables

Accepted Answer

Infeasibility in linear programming problems occurs when one or more of the artificial variables remain in the final solution with a positive value, indicating that the original problem has no feasible solution within the given constraints.

Question 3

A simplex tableau is shown below.  ​ 
a.
Do one more iteration of the simplex procedure.
b.
What is the current complete solution?
c.
Is this solution optimal? Why or why not?

Accepted Answer

The answer of A simplex tableau is shown below. ...

Question 4

Comment on the solution shown in this simplex tableau.

Accepted Answer

The answer of Comment on the solution shown in this...

Question 5

Unit columns are used to identify

Accepted Answer

Unit columns are used to identify the basic variables in a linear programming tableau. Each unit column corresponds to a basic variable, with a single 1 in the row of the basic variable and 0s elsewhere.

Question 6

In the simplex method, a tableau is optimal only if all the c_j − z_j values are

Accepted Answer

In the simplex method, the c_j − z_j values represent the reduced costs. In order to determine if a tableau is optimal, we need to check that all reduced costs are zero or negative, as this means that we cannot improve the current solution by increasing the value of any nonbasic variable. Therefore, choice A is correct. Choice B is incorrect because there may be negative reduced costs. Choices C and D are incorrect because the reduced costs cannot be positive in an optimal tableau.

Question 7

The values in the c_j − z_j , or net evaluation, row indicate

Accepted Answer

The c_j − z_j values indicate the net change in the objective function value if one unit of the corresponding variable enters the basis.

Question 8

Given the following initial simplex tableau  ​ 
a.What variables form the basis?
b.What are the current values of the decision variables?
c.What is the current value of the objective function?
d.Which variable will be made positive next, and what will its value be?Which variable that is currently positive will become 0?
f.What value will the objective function have next?

Accepted Answer

The answer of Given the following initial simplex tableau ...

Question 9

Determine from a review of the following tableau whether the linear programming problem has multiple optimal solutions.

Accepted Answer

The answer of Determine from a review of the following...

Question 10

A simplex table is shown below. a.What is the current complete solution? b.The 32/5 for z₁ is composed of 0 + 8(4/5) + 0. Explain the meaning of this number. c.Explain the meaning of the −12/5 value for c ₂ − z₂.

Accepted Answer

The answer of A simplex table is shown below. ...

Question 11

What coefficient is assigned to an artificial variable in the objective function?

Accepted Answer

The answer of What coefficient is assigned to an artificial...

Question 12

A minimization problem with four decision variables, two greater-than-or-equal-to constraints, and one equality constraint will have

Accepted Answer

In a minimization problem with two greater-than-or-equal-to constraints, each constraint requires a surplus variable. The equality constraint requires an artificial variable. Thus, there are 2 surplus variables and 3 artificial variables (one for each constraint). The number of variables in the basis is equal to the number of constraints, which is 3.

Question 13

Write the following problem in tableau form. Which variables would be in the initial basic solution? Min Z = −3x₁ + x₂ + x₃ s.t. x₁ − 2x₂ + x₃ ≤ 11 −4 x₁ + x₂ + 2x₃ ≥ 3 2x₁ − x₃ ≥ −1

Accepted Answer

The answer of Write the following problem in tableau form....

Question 14

The purpose of the tableau form is to provide

Accepted Answer

The tableau form in linear programming is used to find an initial basic feasible solution, which is a starting point for the simplex method to find the optimal solution.

Question 15

An alternative optimal solution is indicated when in the simplex tableau

Accepted Answer

An alternative optimal solution is indicated when a non-basic variable has a value of zero in the c_j − z_j row. This means that the non-basic variable can be brought into the basis without changing the value of the objective function.

Question 16

Write the following problem in tableau form. Which variables would be in the initial basic solution? Min Z = 3x₁ + 8x₂ s.t. x₁ + x₂ ≤ 200 x₁ ≤ 80 x₂ ≤ 60

Accepted Answer

The answer of Write the following problem in tableau form....

Question 17

When there is a tie between two or more variables for removal from the simplex tableau,

Accepted Answer

A tie in the simplex tableau for removal indicates degeneracy, where multiple solutions exist, and the algorithm may cycle without progress.

Question 18

Solve the following problem by the simplex method. Max 14x₁ + 14.5x₂ + 18x₃ s.t. x₁ + 2x₂ + 2.5x₃ ≤ 50 x₁ + x₂ + 1.5x₃ ≤ 30 x₁ , x₂ , x₃ ≥ 0

Accepted Answer

The answer of Solve the following problem by the simplex...

Question 19

Solve the following problem by the simplex method. Max 100x₁ + 120x₂ + 85x₃ s.t. 3x₁ + 1x₂ + 6x₃ ≤ 120 5x₁ + 8x₂ + 2x₃ ≤ 160 x₁ , x₂ , x₃ ≥ 0

Accepted Answer

The answer of Solve the following problem by the simplex...

Question 20

Which of the following is not a step that is necessary to prepare a linear programming problem for solution using the simplex method?

Accepted Answer

Elementary row and column operations are not necessary for preparing a linear programming problem for the simplex method. These operations are typically used in solving systems of equations, not in setting up a linear programming problem.

Quiz 17: Linear Programming: Simplex Method

Write the following problem in tableau form. Which variables would be in the initial basis? Max x₁ + 2x₂ s.t. 3x₁ + 4x₂ ≤ 100 2x₁ + 3.5x₂ ≥ 60 2x₁ − 1x₂ = 4 x₁ , x₂ ≥ 0

Infeasibility exists when one or more of the artificial variables

A simplex tableau is shown below. a. Do one more iteration of the simplex procedure. b. What is the current complete solution? c. Is this solution optimal? Why or why not?

Comment on the solution shown in this simplex tableau.

Unit columns are used to identify

In the simplex method, a tableau is optimal only if all the c_j − z_j values are

The values in the c_j − z_j , or net evaluation, row indicate

Determine from a review of the following tableau whether the linear programming problem has multiple optimal solutions.

A simplex table is shown below. a.What is the current complete solution? b.The 32/5 for z₁ is composed of 0 + 8(4/5) + 0. Explain the meaning of this number. c.Explain the meaning of the −12/5 value for c ₂ − z₂.

What coefficient is assigned to an artificial variable in the objective function?

A minimization problem with four decision variables, two greater-than-or-equal-to constraints, and one equality constraint will have

Write the following problem in tableau form. Which variables would be in the initial basic solution? Min Z = −3x₁ + x₂ + x₃ s.t. x₁ − 2x₂ + x₃ ≤ 11 −4 x₁ + x₂ + 2x₃ ≥ 3 2x₁ − x₃ ≥ −1

The purpose of the tableau form is to provide

An alternative optimal solution is indicated when in the simplex tableau

Write the following problem in tableau form. Which variables would be in the initial basic solution? Min Z = 3x₁ + 8x₂ s.t. x₁ + x₂ ≤ 200 x₁ ≤ 80 x₂ ≤ 60

When there is a tie between two or more variables for removal from the simplex tableau,

Solve the following problem by the simplex method. Max 14x₁ + 14.5x₂ + 18x₃ s.t. x₁ + 2x₂ + 2.5x₃ ≤ 50 x₁ + x₂ + 1.5x₃ ≤ 30 x₁ , x₂ , x₃ ≥ 0

Solve the following problem by the simplex method. Max 100x₁ + 120x₂ + 85x₃ s.t. 3x₁ + 1x₂ + 6x₃ ≤ 120 5x₁ + 8x₂ + 2x₃ ≤ 160 x₁ , x₂ , x₃ ≥ 0

Which of the following is not a step that is necessary to prepare a linear programming problem for solution using the simplex method?

Quiz 17: Linear Programming: Simplex Method

Write the following problem in tableau form. Which variables would be in the initial basis? Max x1 + 2x2 s.t. 3x1 + 4x2 ≤ 100 2x1 + 3.5x2 ≥ 60 2x1 − 1x2 = 4 x1 , x2 ≥ 0

Infeasibility exists when one or more of the artificial variables

A simplex tableau is shown below. ​ a. Do one more iteration of the simplex procedure. b. What is the current complete solution? c. Is this solution optimal? Why or why not?

Comment on the solution shown in this simplex tableau.

Unit columns are used to identify

In the simplex method, a tableau is optimal only if all the cj − zj values are

The values in the cj − zj , or net evaluation, row indicate

Determine from a review of the following tableau whether the linear programming problem has multiple optimal solutions.

A simplex table is shown below. ​ a.What is the current complete solution? b.The 32/5 for z1 is composed of 0 + 8(4/5) + 0. Explain the meaning of this number. c.Explain the meaning of the −12/5 value for c 2 − z2.

What coefficient is assigned to an artificial variable in the objective function?

A minimization problem with four decision variables, two greater-than-or-equal-to constraints, and one equality constraint will have

Write the following problem in tableau form. Which variables would be in the initial basic solution? Min Z = −3x1 + x2 + x3 s.t. x1 − 2x2 + x3 ≤ 11 −4 x1 + x2 + 2x3 ≥ 3 2x1 − x3 ≥ −1

The purpose of the tableau form is to provide

An alternative optimal solution is indicated when in the simplex tableau

Write the following problem in tableau form. Which variables would be in the initial basic solution? Min Z = 3x1 + 8x2 s.t. x1 + x2 ≤ 200 x1 ≤ 80 x2 ≤ 60

When there is a tie between two or more variables for removal from the simplex tableau,

Solve the following problem by the simplex method. Max 14x1 + 14.5x2 + 18x3 s.t. x1 + 2x2 + 2.5x3 ≤ 50 x1 + x2 + 1.5x3 ≤ 30 x1 , x2 , x3 ≥ 0

Solve the following problem by the simplex method. Max 100x1 + 120x2 + 85x3 s.t. 3x1 + 1x2 + 6x3 ≤ 120 5x1 + 8x2 + 2x3 ≤ 160 x1 , x2 , x3 ≥ 0

Which of the following is not a step that is necessary to prepare a linear programming problem for solution using the simplex method?

Write the following problem in tableau form. Which variables would be in the initial basis? Max x₁ + 2x₂ s.t. 3x₁ + 4x₂ ≤ 100 2x₁ + 3.5x₂ ≥ 60 2x₁ − 1x₂ = 4 x₁ , x₂ ≥ 0

A simplex tableau is shown below. a. Do one more iteration of the simplex procedure. b. What is the current complete solution? c. Is this solution optimal? Why or why not?

In the simplex method, a tableau is optimal only if all the c_j − z_j values are

The values in the c_j − z_j , or net evaluation, row indicate

A simplex table is shown below. a.What is the current complete solution? b.The 32/5 for z₁ is composed of 0 + 8(4/5) + 0. Explain the meaning of this number. c.Explain the meaning of the −12/5 value for c ₂ − z₂.

Write the following problem in tableau form. Which variables would be in the initial basic solution? Min Z = −3x₁ + x₂ + x₃ s.t. x₁ − 2x₂ + x₃ ≤ 11 −4 x₁ + x₂ + 2x₃ ≥ 3 2x₁ − x₃ ≥ −1

Write the following problem in tableau form. Which variables would be in the initial basic solution? Min Z = 3x₁ + 8x₂ s.t. x₁ + x₂ ≤ 200 x₁ ≤ 80 x₂ ≤ 60

Solve the following problem by the simplex method. Max 14x₁ + 14.5x₂ + 18x₃ s.t. x₁ + 2x₂ + 2.5x₃ ≤ 50 x₁ + x₂ + 1.5x₃ ≤ 30 x₁ , x₂ , x₃ ≥ 0

Solve the following problem by the simplex method. Max 100x₁ + 120x₂ + 85x₃ s.t. 3x₁ + 1x₂ + 6x₃ ≤ 120 5x₁ + 8x₂ + 2x₃ ≤ 160 x₁ , x₂ , x₃ ≥ 0