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The document summarizes the results of solving a linear programming problem with 2 variables and 6 constraints. The optimal solution was found at the first step with an objective value of 660. The values of the variables X1 and X2 at the optimal solution are 70 and 90, respectively. Ranges for the objective coefficients and right-hand side values are provided where the basis remains unchanged.
![2 0.0000000E+00 0.3333333
3 0.0000000E+00 2.333333
4 30.00000 0.0000000E+00
5 70.00000 0.0000000E+00
6 90.00000 0.0000000E+00
Ranges in which the basis is unchanged:
Objective Coefficient Ranges
Current Allowable Allowable
Variable Coefficient Increase Decrease
X1 3.000000 7.000000 0.5000000
X2 5.000000 1.000000 3.500000
Righthand Side Ranges
Row Current Allowable Allowable
RHS IncreaseDecrease
2 230.0000 270.0000 90.00000
3 250.0000 45.00000 135.0000
4 120.0000 INFINITY 30.00000
5 0.0 70.00000 INFINITY
6 0.0 90.00000 INFINITY
1]max=3*x1+5*x2;
2]2*x1+x2<=230;
3]x1+2*x2<=250;](https://image.slidesharecdn.com/rows-121120015741-phpapp01/85/Rows-2-320.jpg)
![4]x2<=120;
5]x1>=0;
6]x2>=0;
7]
http://es.calameo.com/read/00114496451c6f9fe7a29](https://image.slidesharecdn.com/rows-121120015741-phpapp01/85/Rows-3-320.jpg)
Rows
- 1. Rows= 6 Vars= 2 No. integer vars= 0 ( all are linear) Nonzeros= 12 Constraint nonz= 7( 5 are +- 1) Density=0.667 Smallest and largest elements in absolute value= 1.00000 250.000 No. < : 3 No. =: 0 No. > : 2, Obj=MAX, GUBs<= 2 Single cols= 0 Optimal solution found at step: 1 Objective value: 660.0000 Variable Value Reduced Cost X1 70.00000 0.0000000E+00 X2 90.00000 0.0000000E+00 Row Slack or Surplus Dual Price 1 660.0000 1.000000 2 0.0000000E+00 0.3333333 3 0.0000000E+00 2.333333 4 30.00000 0.0000000E+00 5 70.00000 0.0000000E+00 6 90.00000 0.0000000E+00 Variable ValueReducedCost X1 70.00000 0.0000000E+00 X2 90.00000 0.0000000E+00 Row Slack or Surplus Dual Price 1 660.0000 1.000000
- 2. 2 0.0000000E+00 0.3333333 3 0.0000000E+00 2.333333 4 30.00000 0.0000000E+00 5 70.00000 0.0000000E+00 6 90.00000 0.0000000E+00 Ranges in which the basis is unchanged: Objective Coefficient Ranges Current Allowable Allowable Variable Coefficient Increase Decrease X1 3.000000 7.000000 0.5000000 X2 5.000000 1.000000 3.500000 Righthand Side Ranges Row Current Allowable Allowable RHS IncreaseDecrease 2 230.0000 270.0000 90.00000 3 250.0000 45.00000 135.0000 4 120.0000 INFINITY 30.00000 5 0.0 70.00000 INFINITY 6 0.0 90.00000 INFINITY 1]max=3*x1+5*x2; 2]2*x1+x2<=230; 3]x1+2*x2<=250;