Consider the following linear programming problem: Maximize 40 X1 + 30 X2 + 60X3 Subject to: X1 + X2 + X3 ≥ 90 12 X1 + 8 X2 + 10 X3 ≤ 1500 X1 ,X2 ,X3 ≥ 0 How many slack,surplus,and artificial variables would be necessary if the simplex were used to solve this problem?

A) 3 slack,3 surplus,and 3 artificial B) 1 slack,2 surplus,and 2 artificial C) 1 slack,4 surplus,and 4 artificial D) 1 slack,1 surplus,and 1 artificial E) None of the above A) 3 slack,3 surplus,and 3 artificial B) 1 slack,2 surplus,and 2 artificial C) 1 slack,4 surplus,and 4 artificial D) 1 slack,1 surplus,and 1 artificial E) None of the above D

A) that is a maximization problem,the dual is a minimization problem. B) the right-hand side quantities become the dual's objective function coefficients. C) constraint inequality signs are reversed in the dual. D) the transpose of the constraint coefficients become the dual's constraint coefficients. E) All of the above A) that is a maximization problem,the dual is a minimization problem. B) the right-hand side quantities become the dual's objective function coefficients. C) constraint inequality signs are reversed in the dual. D) the transpose of the constraint coefficients become the dual's constraint coefficients. E) All of the above

Exam 22: Linear Programming: The Simplex Method

Consider the following linear programming problem: Maximize 40 X₁ + 30 X₂ + 60X₃ Subject to: X₁ + X₂ + X₃ ≥ 90 12 X₁ + 8 X₂ + 10 X₃ ≤ 1500 X₁ ,X₂ ,X₃ ≥ 0 How many slack,surplus,and artificial variables would be necessary if the simplex were used to solve this problem?

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Question 1

Correct Answer:

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Upon retirement,Mr.Klaws started to make two types of children's wooden toys in his shop.Wuns yield a variable profit of $8 each,and Toos have a contribution margin of $9 each.Even though his electric saw overheats,he can make 7 Wuns or 14 Toos each day.Since he doesn't have equipment for drying the lacquer finish he puts on the toys,the drying operation limits him to 16 Wuns or 8 Toos per day.The final tableau for Mr.Klaws' problem would be: (a)What would the value be of an additional unit of constraint #1? (b)What would the value be of an additional unit of constraint #2?

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Question 2

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(a)$7/3
(b)$10/3

The simplex method begins with an initial feasible solution in which all real variables are set equal to 0.

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Question 3

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True

How should the constraint,5X - 2Y = 6,be converted into simplex tableau form?

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Question 4

Artificial variables can be used in both maximization and minimization problems but are most often used in minimization problems.

(True/False)

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Question 5

In 1984,who developed an alternative to the simplex algorithm,which often takes significantly less computer time to solve very large-scale LP problems?

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Question 6

Table M7-3 -According to Table M7-3,which is the final simplex tableau for a problem with two variables and two constraints,what can be said about the optimal solution and the constraints?

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Question 7

Dual variables represent the potential value of resources.

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Question 8

Table M7-2 -According to Table M7-2,which is a summarized solution output from simplex analysis,the optimal solution to this problem is

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Question 9

The constraint 5 X₁ + 6 X₂ = 30,when converted to an = constraint for use in the simplex algorithm,will be 5 X₁ + 6 X₂ - A = 30.

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Question 10

Convert the following linear program into a simplex model form: Maximize 8X + 10Y Subject to: 5X + 3Y ≤ 34 2X + 3Y = 22 X ≥ 3 X,Y ≥ 0

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Question 11

In solving a linear programming minimization problem using the simplex method,

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Question 12

For every primal

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Question 13

The constraint 5X₁ + 6X₂ ≥ 30,when converted to an = constraint for use in the simplex algorithm,will be 5 X₁ + 6 X₂ - S = 30.

(True/False)

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Question 14

Table M7-3 -According to Table M7-3,which is the final simplex tableau for a problem with two variables and two constraints,what are the values for all the variables in this solution?

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Question 15

Right-hand side ranging

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Question 16

Given the following dual linear program,write the primal program. Maximize 3U₁ + 2U₂ Subject to: 7U₁ - 2U₂ ≤ 0 5U₁ + U₂ ≤ 10 U₁ + 7U₂ ≤ 12 U₁,U₂ ≥ 0

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Question 17

An infeasible solution is indicated when all the C_j - Z_j row entries are of the proper sign to imply optimality,but an artificial variable remains in the solution.

(True/False)

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Question 18

In a maximization problem,the C_j - Z_j row gives the net loss from introducing one unit of each variable into the solution.

(True/False)

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Question 19

A basic feasible solution to a system of n equations is found by setting n variables equal to 0 and solving for the other variables.

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Question 20

Showing 1 - 20 of 100

Exam 22: Linear Programming: The Simplex Method

Consider the following linear programming problem: Maximize 40 X1 + 30 X2 + 60X3 Subject to: X1 + X2 + X3 ≥ 90 12 X1 + 8 X2 + 10 X3 ≤ 1500 X1 ,X2 ,X3 ≥ 0 How many slack,surplus,and artificial variables would be necessary if the simplex were used to solve this problem?

The simplex method begins with an initial feasible solution in which all real variables are set equal to 0.

How should the constraint,5X - 2Y = 6,be converted into simplex tableau form?

Artificial variables can be used in both maximization and minimization problems but are most often used in minimization problems.

In 1984,who developed an alternative to the simplex algorithm,which often takes significantly less computer time to solve very large-scale LP problems?

Table M7-3 -According to Table M7-3,which is the final simplex tableau for a problem with two variables and two constraints,what can be said about the optimal solution and the constraints?

Dual variables represent the potential value of resources.

Table M7-2 -According to Table M7-2,which is a summarized solution output from simplex analysis,the optimal solution to this problem is

The constraint 5 X1 + 6 X2 = 30,when converted to an = constraint for use in the simplex algorithm,will be 5 X1 + 6 X2 - A = 30.

Convert the following linear program into a simplex model form: Maximize 8X + 10Y Subject to: 5X + 3Y ≤ 34 2X + 3Y = 22 X ≥ 3 X,Y ≥ 0

In solving a linear programming minimization problem using the simplex method,

For every primal

The constraint 5X1 + 6X2 ≥ 30,when converted to an = constraint for use in the simplex algorithm,will be 5 X1 + 6 X2 - S = 30.

Table M7-3 -According to Table M7-3,which is the final simplex tableau for a problem with two variables and two constraints,what are the values for all the variables in this solution?

Right-hand side ranging

Given the following dual linear program,write the primal program. Maximize 3U1 + 2U2 Subject to: 7U1 - 2U2 ≤ 0 5U1 + U2 ≤ 10 U1 + 7U2 ≤ 12 U1,U2 ≥ 0

An infeasible solution is indicated when all the Cj - Zj row entries are of the proper sign to imply optimality,but an artificial variable remains in the solution.

In a maximization problem,the Cj - Zj row gives the net loss from introducing one unit of each variable into the solution.

A basic feasible solution to a system of n equations is found by setting n variables equal to 0 and solving for the other variables.

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Consider the following linear programming problem: Maximize 40 X₁ + 30 X₂ + 60X₃ Subject to: X₁ + X₂ + X₃ ≥ 90 12 X₁ + 8 X₂ + 10 X₃ ≤ 1500 X₁ ,X₂ ,X₃ ≥ 0 How many slack,surplus,and artificial variables would be necessary if the simplex were used to solve this problem?

The constraint 5 X₁ + 6 X₂ = 30,when converted to an = constraint for use in the simplex algorithm,will be 5 X₁ + 6 X₂ - A = 30.

The constraint 5X₁ + 6X₂ ≥ 30,when converted to an = constraint for use in the simplex algorithm,will be 5 X₁ + 6 X₂ - S = 30.

Given the following dual linear program,write the primal program. Maximize 3U₁ + 2U₂ Subject to: 7U₁ - 2U₂ ≤ 0 5U₁ + U₂ ≤ 10 U₁ + 7U₂ ≤ 12 U₁,U₂ ≥ 0

An infeasible solution is indicated when all the C_j - Z_j row entries are of the proper sign to imply optimality,but an artificial variable remains in the solution.

In a maximization problem,the C_j - Z_j row gives the net loss from introducing one unit of each variable into the solution.