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Exam 17: Linear Programming: Simplex Method

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Question 21

True/False

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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.

A) True
B) False

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Question 22

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An alternative optimal solution is indicated when,in the simplex tableau,a

A) nonbasic variable has a value of zero in the c_j − z_j row.
B) basic variable has a positive value in the c_j − z_j row.
C) basic variable has a value of zero in the c_j − z_j row.
D) nonbasic variable has a positive value in the c_j − z_j row.

E) A) and B)
F) B) and D)

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Question 23

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Jackie Quinn developed the following LP formulation for a problem she is working on and now needs to create an initial simplex tableau.Create the initial simplex tableau.​ Min 75x_l + 45x₂ s.t.3x_l + 2x₂ > 10 x_l + 6x₂ > 15 ​

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

The variable to remove from the current basis is the variable with the smallest positive c_j − z_j value.

Solve the following problem by the simplex method.

The simplex method is an iterative procedure for moving from one basic feasible solution (an extreme point)to another until the optimal solution is reached.

A basic feasible solution is a basic solution that

A simplex tableau 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.

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

What type of solution is shown in this simplex tableau?

An operations research analyst for a communications company has the following LP problem and wants to solve it using the simplex method.​ Max 50x₁ + 20x₂ s.t.2x₁ + x₂ < 200 x₁ + x₂ < 350 x_l + 2x₂ < 275

Write the following problem in tableau form.Which variables would be in the initial basic solution?

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

Identify the type of solution shown in this simplex tableau. ​

Joe Forrester,an operations analyst for a manufacturing company,developed the following LP formulation.From it,create an initial simplex tableau.​ Max 40x_l + 30x₂ + 50x₃ s.t.2x_l + 3x₂ + 4x₃ < 200 x₁ + 2x₂ + 2x₃ < 300 3x_l + x₂ + 5x₃ < 500

Solve the following problem by the simplex method.

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

Unit columns are used to identify the

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