Question: Given the following LP problem formulation and output data, perform the analysis below. Max. 100X1 + 120X2 + 150X3 + 125X4 s.t X1 + 2X2
Given the following LP problem formulation and output data, perform the analysis below.
Max. 100X1 + 120X2 + 150X3 + 125X4
s.t X1 + 2X2 + 2X3 + 2X4 < 108 (C1)
3X1 + 5X2 + X4 < 120 (C2)
X1 + X3 < 25 (C3)
X2 + X3 + X4 > 50 (C4)
OPTIMAL SOLUTION:
Objective Function Value = 7475.000
| Variable | Value | Reduced Costs | ||
| X1 | 8.000 | 0.500 | ||
| X2 | 0.000 | 5.000 | ||
| X3 | 17.000 | 0.000 | ||
| X4 | *A | 0.000 | ||
|
| Constraint | Slack / Surplus | Dual Prices |
|
|
| 1 | 0.000 | *B |
|
|
| 2 | 63.000 | 0.000 |
|
|
| 3 | *C | 25.000 |
|
|
| 4 | 0.000 | -25.000 |
|
Objective Co-efficient Ranges
| Variable | Lower Limit | Current Value | Upper Limit |
| X1 | 87.500 | 100.000 | No Upper Limit |
| X2 | No lower limit | 120.000 | 125.000 |
| X3 | 125.000 | 150.000 | 162.500 |
| X4 | 120.000 | 125.000 | 150.000 |
Right Hand Side Ranges
| Constraint | Lower Limit | Current Value | Upper Limit |
| 1 | 100.000 | 108.000 | 123.750 |
| 2 | 57.000 | 120.000 | No Upper Limit |
| 3 | 8.000 | 25.000 | 58.000 |
| 4 | 41.000 | 50.000 | 54.000 |
- Find *A
- How much of constraint C2 is used?
- In each of the following, calculate the resulting change in the objective function, if possible and show you calculations. If not possible, explain why not.
- The obj.func.co-eff of X4 increases from 125 to 135.
- The level of C4 decreases from 50 to 42.
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