Question 1

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

a.s₁, s₂ , s₃ B.x₁ = 0, x₂ = 0, x₃ = 0, s₁ = 80, s₂ = 250, s₃ = 20 C.0 D.x₃, 10 E.s₃ F.z = 120

Question 2

The purpose of the tableau form is to provide

Accepted Answer

A)   infeasible solution.
B)   optimal infeasible solution.
C)   initial basic feasible solution.
D)   degenerate solution. C

Question 3

If a variable is not in the basis, its value is 0.

Accepted Answer

A) True 
 B)False  True

Question 4

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 5

Comment on the solution shown in this simplex tableau.

Accepted Answer

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

Question 6

Coefficients in a nonbasic column in a simplex tableau indicate the amount of decrease in the current basic variables when the value of the nonbasic variable is increased from 0 to 1.

Accepted Answer

A) True 
 B)False

Question 7

The purpose of row operations is to create a unit column for the entering variable while maintaining unit columns for the remaining basic variables.

Accepted Answer

A) True 
 B)False

Question 8

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 9

To determine a basic solution set of n−m, the variables equal to zero and solve the m linear constraint equations for the remaining m variables.

Accepted Answer

A) True 
 B)False

Question 10

The basic solution to a problem with three equations and four variables would assign a value of 0 to

Accepted Answer

A)   0 variables.
B)   1 variable.
C)   3 variables.
D)   7 variables.

Question 11

Algebraic methods such as the simplex method are used to solve

Accepted Answer

A)   nonlinear programming problems.
B)   any size linear programming problem.
C)   programming problems under uncertainty.
D)   graphical models.

Question 12

What is an artificial variable? Why is it necessary?

Accepted Answer

The answer of What is an artificial variable? Why is...

Question 13

A solution is optimal when all values in the cj − zj row of the simplex tableau are either zero or positive.

Accepted Answer

A) True 
 B)False

Question 14

​For each of the special cases of infeasibility, unboundedness, and alternate optimal solutions, tell what you would do next with your linear programming model if the case occurred.

Accepted Answer

The answer of ​For each of the special cases of...

Question 15

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

Accepted Answer

A)   post-optimality analysis is required.
B)   their dual prices will be equal.
C)   converting the pivot element will break the tie.
D)   a condition of degeneracy is present.

Question 16

In a simplex tableau, there is a variable associated with each column and both a constraint and a basic variable associated with each row.

Accepted Answer

A) True 
 B)False

Question 17

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 18

A basic solution and a basic feasible solution

Accepted Answer

A)   are the same thing.
B)   differ in the number of variables allowed to be zero.
C)   describe interior points and exterior points, respectively.
D)   differ in their inclusion of nonnegativity restrictions.

Question 19

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 20

​A student in a Management Science class developed this initial tableau for a maximization problem and ​
now wants to perform row operations to obtain the next tableau and check for an optimal solution.
​  ​

Accepted Answer

The answer of ​A student in a Management Science class...

Exam 17: Linear Programming: Simplex Method

The purpose of the tableau form is to provide

If a variable is not in the basis, its value is 0.

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.

Comment on the solution shown in this simplex tableau.

Coefficients in a nonbasic column in a simplex tableau indicate the amount of decrease in the current basic variables when the value of the nonbasic variable is increased from 0 to 1.

The purpose of row operations is to create a unit column for the entering variable while maintaining unit columns for the remaining basic 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?

To determine a basic solution set of n−m, the variables equal to zero and solve the m linear constraint equations for the remaining m variables.

The basic solution to a problem with three equations and four variables would assign a value of 0 to

Algebraic methods such as the simplex method are used to solve

What is an artificial variable? Why is it necessary?

A solution is optimal when all values in the c_j − z_j row of the simplex tableau are either zero or positive.

For each of the special cases of infeasibility, unboundedness, and alternate optimal solutions, tell what you would do next with your linear programming model if the case occurred.

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

In a simplex tableau, there is a variable associated with each column and both a constraint and a basic variable associated with each row.

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

A basic solution and a basic feasible solution

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

A student in a Management Science class developed this initial tableau for a maximization problem and now wants to perform row operations to obtain the next tableau and check for an optimal solution.

Exam 17: Linear Programming: Simplex Method

The purpose of the tableau form is to provide

If a variable is not in the basis, its value is 0.

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.

Comment on the solution shown in this simplex tableau.

Coefficients in a nonbasic column in a simplex tableau indicate the amount of decrease in the current basic variables when the value of the nonbasic variable is increased from 0 to 1.

The purpose of row operations is to create a unit column for the entering variable while maintaining unit columns for the remaining basic 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?

To determine a basic solution set of n−m, the variables equal to zero and solve the m linear constraint equations for the remaining m variables.

The basic solution to a problem with three equations and four variables would assign a value of 0 to

Algebraic methods such as the simplex method are used to solve

What is an artificial variable? Why is it necessary?

A solution is optimal when all values in the cj − zj row of the simplex tableau are either zero or positive.

​For each of the special cases of infeasibility, unboundedness, and alternate optimal solutions, tell what you would do next with your linear programming model if the case occurred.

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

In a simplex tableau, there is a variable associated with each column and both a constraint and a basic variable associated with each row.

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

A basic solution and a basic feasible solution

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

​A student in a Management Science class developed this initial tableau for a maximization problem and ​ now wants to perform row operations to obtain the next tableau and check for an optimal solution. ​ ​

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.

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?

A solution is optimal when all values in the c_j − z_j row of the simplex tableau are either zero or positive.

For each of the special cases of infeasibility, unboundedness, and alternate optimal solutions, tell what you would do next with your linear programming model if the case occurred.

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

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

A student in a Management Science class developed this initial tableau for a maximization problem and now wants to perform row operations to obtain the next tableau and check for an optimal solution.