The given table is: z x 1 x 2 x 3 x 4 x 5 x 6 rhs 1 c 1 c 2 0 0 0 0 10 0 4 a 1 1 0 a 2 0 b 0 -1 -5 0 1 -1 0 2 0 a 3 -3 0 0 -4 1 3 The current solution is optimum if and only if c 1 ≥0, c 2 ≥0, and b≥0...

Question

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Answer 1

Expert Solution & Answer

Chapter 4, Problem 18RP

a.

Explanation of Solution

The given table is:

z x₁ x₂ x₃ x₄ x₅ x₆ rhs
1 c₁ c₂ 0 0 0 0 10
0 4 a₁ 1 0 a₂ 0 b
0 -1 -5 0 1 -1 0 2
0 a₃ -3 0 0 -4 1 3

The current solution is optimum if and only if c₁≥0, c₂≥0, and b≥0...

b.

Explanation of Solution

Given statement: the basic feasible solution in not a basic feasible solution...

c.

Explanation of Solution

Given statement: the current basic solution is a degenerate basic feasible solution...

d.

Explanation of Solution

Given statement: the current basic solution is feasible, but the LP is unbounded.

Condition: in this case, if the LP is unbounded, then c₂<0...

e.

Explanation of Solution

Here, b≥0 makes the solution as basic feasible solution.

The objective function value can be improved by replacing x₆ as the basic variable with x₁ means that x₁ enters the basis and x₆ leaves the basis...

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 2

Expert Solution & Answer

Chapter 4, Problem 18RP

a.

Explanation of Solution

The given table is:

z x₁ x₂ x₃ x₄ x₅ x₆ rhs
1 c₁ c₂ 0 0 0 0 10
0 4 a₁ 1 0 a₂ 0 b
0 -1 -5 0 1 -1 0 2
0 a₃ -3 0 0 -4 1 3

The current solution is optimum if and only if c₁≥0, c₂≥0, and b≥0...

b.

Explanation of Solution

Given statement: the basic feasible solution in not a basic feasible solution...

c.

Explanation of Solution

Given statement: the current basic solution is a degenerate basic feasible solution...

d.

Explanation of Solution

Given statement: the current basic solution is feasible, but the LP is unbounded.

Condition: in this case, if the LP is unbounded, then c₂<0...

e.

Explanation of Solution

Here, b≥0 makes the solution as basic feasible solution.

The objective function value can be improved by replacing x₆ as the basic variable with x₁ means that x₁ enters the basis and x₆ leaves the basis...

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Expert Solution & Answer

Chapter 4, Problem 18RP

a.

Explanation of Solution

The given table is:

z x₁ x₂ x₃ x₄ x₅ x₆ rhs
1 c₁ c₂ 0 0 0 0 10
0 4 a₁ 1 0 a₂ 0 b
0 -1 -5 0 1 -1 0 2
0 a₃ -3 0 0 -4 1 3

The current solution is optimum if and only if c₁≥0, c₂≥0, and b≥0...

b.

Explanation of Solution

Given statement: the basic feasible solution in not a basic feasible solution...

c.

Explanation of Solution

Given statement: the current basic solution is a degenerate basic feasible solution...

d.

Explanation of Solution

Given statement: the current basic solution is feasible, but the LP is unbounded.

Condition: in this case, if the LP is unbounded, then c₂<0...

e.

Explanation of Solution

Here, b≥0 makes the solution as basic feasible solution.

The objective function value can be improved by replacing x₆ as the basic variable with x₁ means that x₁ enters the basis and x₆ leaves the basis...

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Expert Solution & Answer

Chapter 4, Problem 18RP

a.

Explanation of Solution

The given table is:

z x₁ x₂ x₃ x₄ x₅ x₆ rhs
1 c₁ c₂ 0 0 0 0 10
0 4 a₁ 1 0 a₂ 0 b
0 -1 -5 0 1 -1 0 2
0 a₃ -3 0 0 -4 1 3

The current solution is optimum if and only if c₁≥0, c₂≥0, and b≥0...

b.

Explanation of Solution

Given statement: the basic feasible solution in not a basic feasible solution...

c.

Explanation of Solution

Given statement: the current basic solution is a degenerate basic feasible solution...

d.

Explanation of Solution

Given statement: the current basic solution is feasible, but the LP is unbounded.

Condition: in this case, if the LP is unbounded, then c₂<0...

e.

Explanation of Solution

Here, b≥0 makes the solution as basic feasible solution.

The objective function value can be improved by replacing x₆ as the basic variable with x₁ means that x₁ enters the basis and x₆ leaves the basis...

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Expert Solution & Answer

Answer 6

Expert Solution & Answer

Answer 7

Chapter 4, Problem 18RP

a.

Explanation of Solution

The given table is:

z x₁ x₂ x₃ x₄ x₅ x₆ rhs
1 c₁ c₂ 0 0 0 0 10
0 4 a₁ 1 0 a₂ 0 b
0 -1 -5 0 1 -1 0 2
0 a₃ -3 0 0 -4 1 3

The current solution is optimum if and only if c₁≥0, c₂≥0, and b≥0...

b.

Explanation of Solution

Given statement: the basic feasible solution in not a basic feasible solution...

c.

Explanation of Solution

Given statement: the current basic solution is a degenerate basic feasible solution...

d.

Explanation of Solution

Given statement: the current basic solution is feasible, but the LP is unbounded.

Condition: in this case, if the LP is unbounded, then c₂<0...

e.

Explanation of Solution

Here, b≥0 makes the solution as basic feasible solution.

The objective function value can be improved by replacing x₆ as the basic variable with x₁ means that x₁ enters the basis and x₆ leaves the basis...

Answer 8

Chapter 4, Problem 18RP

a.

Explanation of Solution

The given table is:

z x₁ x₂ x₃ x₄ x₅ x₆ rhs
1 c₁ c₂ 0 0 0 0 10
0 4 a₁ 1 0 a₂ 0 b
0 -1 -5 0 1 -1 0 2
0 a₃ -3 0 0 -4 1 3

The current solution is optimum if and only if c₁≥0, c₂≥0, and b≥0...

Answer 9

Chapter 4, Problem 18RP

a.

Explanation of Solution

The given table is:

z x₁ x₂ x₃ x₄ x₅ x₆ rhs
1 c₁ c₂ 0 0 0 0 10
0 4 a₁ 1 0 a₂ 0 b
0 -1 -5 0 1 -1 0 2
0 a₃ -3 0 0 -4 1 3

The current solution is optimum if and only if c₁≥0, c₂≥0, and b≥0...

Answer 10

b.

Explanation of Solution

Given statement: the basic feasible solution in not a basic feasible solution...

Answer 11

b.

Explanation of Solution

Given statement: the basic feasible solution in not a basic feasible solution...

Answer 12

c.

Explanation of Solution

Given statement: the current basic solution is a degenerate basic feasible solution...

Answer 13

c.

Explanation of Solution

Given statement: the current basic solution is a degenerate basic feasible solution...

Answer 14

d.

Explanation of Solution

Given statement: the current basic solution is feasible, but the LP is unbounded.

Condition: in this case, if the LP is unbounded, then c₂<0...

Answer 15

d.

Explanation of Solution

Given statement: the current basic solution is feasible, but the LP is unbounded.

Condition: in this case, if the LP is unbounded, then c₂<0...

Answer 16

e.

Explanation of Solution

Here, b≥0 makes the solution as basic feasible solution.

The objective function value can be improved by replacing x₆ as the basic variable with x₁ means that x₁ enters the basis and x₆ leaves the basis...

Answer 17

e.

Explanation of Solution

Here, b≥0 makes the solution as basic feasible solution.

The objective function value can be improved by replacing x₆ as the basic variable with x₁ means that x₁ enters the basis and x₆ leaves the basis...

Answer 18

Expert Solution & Answer

Answer 19

Expert Solution & Answer

Answer 20

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Answer 21

Ch. 4.1 - Prob. 1P Ch. 4.1 - Prob. 2P Ch. 4.1 - Prob. 3P Ch. 4.4 - Prob. 1P Ch. 4.4 - Prob. 2P Ch. 4.4 - Prob. 3P Ch. 4.4 - Prob. 4P Ch. 4.4 - Prob. 5P Ch. 4.4 - Prob. 6P Ch. 4.4 - Prob. 7P

The given table is: z x 1 x 2 x 3 x 4 x 5 x 6 rhs 1 c 1 c 2 0 0 0 0 10 0 4 a 1 1 0 a 2 0 b 0 -1 -5 0 1 -1 0 2 0 a 3 -3 0 0 -4 1 3 The current solution is optimum if and only if c 1 ≥0, c 2 ≥0, and b≥0...

Solution Summary: The author states that the current solution is a degenerate basic feasible solution. The objective function value can be improved by replacing x 6 as the basic variable.

Concept explainers

Explanation of Solution

The given table is:

z x₁ x₂ x₃ x₄ x₅ x₆ rhs
1 c₁ c₂ 0 0 0 0 10
0 4 a₁ 1 0 a₂ 0 b
0 -1 -5 0 1 -1 0 2
0 a₃ -3 0 0 -4 1 3

The current solution is optimum if and only if c₁≥0, c₂≥0, and b≥0...

Explanation of Solution

Given statement: the basic feasible solution in not a basic feasible solution...

Explanation of Solution

Given statement: the current basic solution is a degenerate basic feasible solution...

Explanation of Solution

Given statement: the current basic solution is feasible, but the LP is unbounded.

Condition: in this case, if the LP is unbounded, then c₂<0...

Explanation of Solution

Here, b≥0 makes the solution as basic feasible solution.

The objective function value can be improved by replacing x₆ as the basic variable with x₁ means that x₁ enters the basis and x₆ leaves the basis...

Want to see the full answer?

Chapter 4 Solutions

z	x₁	x₂	x₃	x₄	x₅	x₆	rhs
1	c₁	c₂	0	0	0	0	10
0	4	a₁	1	0	a₂	0	b
0	-1	-5	0	1	-1	0	2
0	a₃	-3	0	0	-4	1	3

The given table is: z x 1 x 2 x 3 x 4 x 5 x 6 rhs 1 c 1 c 2 0 0 0 0 10 0 4 a 1 1 0 a 2 0 b 0 -1 -5 0 1 -1 0 2 0 a 3 -3 0 0 -4 1 3 The current solution is optimum if and only if c 1 ≥0, c 2 ≥0, and b≥0...

Solution Summary: The author states that the current solution is a degenerate basic feasible solution. The objective function value can be improved by replacing x 6 as the basic variable.

Concept explainers

Explanation of Solution