Question
The following linear programming problem has been solved by the management scientist. Use the output to answer the questions. LINEAR PROGRAMMING PROBELM MAX 25x1 +
The following linear programming problem has been solved by the management scientist. Use the output to answer the questions.
LINEAR PROGRAMMING PROBELM
MAX 25x1 + 30x2 + 15x3
s.t.
- 4x1 + 5x2 + 8x3 < 1200
- 9x1 + 15x2 + 3x3 < 1500
OPTIMAL SOLUTION
objective Function Value = 4700.000
| variable | value | reduced costs |
| x1 | 140.000 | 0.000 |
| x2 | 0.000 | 10.000 |
| x3 | 80.000 | 0.000 |
| constraint | slack/surplus | dual prices |
| 1 | 0.000 | 1.000 |
| 2 | 0.000 | 2.333 |
OBJECTIVE COEFFICIENT RANGES
| variable | lower limit | current value | upper limit |
| x1 | 19.286 | 25.000 | 45.000 |
| x2 | no | 30.000 | 40.000 |
| x3 | 8.333 | 15.000 | 50.000 |
RIGHT HAND SIDE RANGES
| constraint | lower limit | current value | upper limit |
| 1 | 666.667 | 1200.000 | 4000.000 |
| 2 | 450.000 | 1500.000 | 2700.000 |
a. give the complete optimal solution
b. which constraints are binding?
c. what is the dual price for the second constraint? what interpretation does this have?
d. over what range can the objective function coefficient of x2 vary before a new solution point becomes optimal?
e. by how much can the amount of resource 2 decrease before the dual price will change?
Step by Step Solution
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Step: 1
Solution a The complete optimal solution is x1 140 x2 0 x3 80 b The constraints t...
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Finite Mathematics For Business Economics Life Sciences And Social Sciences
Authors: Raymond Barnett, Michael Ziegler, Karl Byleen, Christopher Stocker
14th Edition
0134862627, 9780134862620
