The optimal solution of this linear programming problem is at the intersection of constraints 1 and 2. Max 3x1 + x2 s.t. 4x1 + x2 ≤ 400 4x1 + 3x2 ≤ 600 x1 + 2x2 ≤ 300 x1, x2 ≥ 0 Over what range can the coefficient of x1 vary before the current solution is no longer optimal? (Round your answers to two decimal places.) Over what range can the coefficient of x2 vary before the current solution is no longer optimal? (Round your answers to two decimal places.) Compute the dual value for the first constraint? Compute the dual value for the second constraint? Compute the dual value for the third constraint?
The optimal solution of this linear programming problem is at the intersection of constraints 1 and 2. Max 3x1 + x2 s.t. 4x1 + x2 ≤ 400 4x1 + 3x2 ≤ 600 x1 + 2x2 ≤ 300 x1, x2 ≥ 0 Over what range can the coefficient of x1 vary before the current solution is no longer optimal? (Round your answers to two decimal places.) Over what range can the coefficient of x2 vary before the current solution is no longer optimal? (Round your answers to two decimal places.) Compute the dual value for the first constraint? Compute the dual value for the second constraint? Compute the dual value for the third constraint?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The optimal solution of this linear programming problem is at the intersection of constraints 1 and 2.
Max 3x1 + x2
| s.t. | ||||
| 4x1 + x2 | ≤ | 400 | ||
| 4x1 + 3x2 | ≤ | 600 | ||
| x1 + 2x2 | ≤ | 300 | ||
| x1, x2 | ≥ | 0 |
Over what range can the coefficient of x1 vary before the current solution is no longer optimal? (Round your answers to two decimal places.)
Over what range can the coefficient of x2 vary before the current solution is no longer optimal? (Round your answers to two decimal places.)
Compute the dual value for the first constraint?
Compute the dual value for the second constraint?
Compute the dual value for the third constraint?
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Transcribed Image Text:The optimal solution of this linear programming problem is at the intersection of constraints 1 and 2.
Max
3x₁ + x₂
s.t.
4x₁ + x₂ ≤ 400
4x₁ + 3x₂ ≤600
X₁ + 2x₂ ≤ 300
X1 X₂20
(a) Over what range can the coefficient of x₁ vary before the current solution is no longer optimal? (Round your answers to two decimal places.)
to 75,
x Your answer cannot be understood or graded. More Information
75,100
(b) Over what range can the coefficient of x₂ vary before the current solution is no longer optimal? (Round your answers to two decimal places.)
0x to 2.25
(c) Compute the dual value for the first constraint.
0.25 X
Compute the dual value for the second constraint.
600 X
Compute the dual value for the third constraint.
275
Solution
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