ejercicios resueltos en lindo

1. Practica de IO
Pregunta 1
LP OPTIMUM FOUND AT STEP 1
OBJECTIVE FUNCTION VALUE
1) 8.000000
VARIABLE VALUE REDUCED COST
X1 4.000000 0.000000
X2 0.000000 0.666667
ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 0.000000
3) 0.000000 0.666667
NO. ITERATIONS= 1
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X1 2.000000 INFINITY 0.500000
X2 2.000000 0.666667 INFINITY
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
2 8.000000 INFINITY 0.000000
3 12.000000 0.000000 12.000000
PREGUNTA 2
LP OPTIMUM FOUND AT STEP 1
OBJECTIVE FUNCTION VALUE
1) 100.0000
VARIABLE VALUE REDUCED COST
X1 0.000000 7.000000
X2 0.000000 6.000000
X3 10.000000 0.000000

2. ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 10.000000
3) 15.000000 0.000000
NO. ITERATIONS= 1
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X1 3.000000 7.000000 INFINITY
X2 4.000000 6.000000 INFINITY
X3 10.000000 INFINITY 6.000000
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
2 10.000000 INFINITY 10.000000
3 15.000000 INFINITY 15.000000
PREGUNTA 3
LP OPTIMUM FOUND AT STEP 1
OBJECTIVE FUNCTION VALUE
1) 36.00000
VARIABLE VALUE REDUCED COST
X1 0.000000 2.000000
X2 0.000000 4.000000
X3 12.000000 0.000000
X4 0.000000 2.000000
ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 3.000000
3) 6.000000 0.000000
4) 4.000000 0.000000
NO. ITERATIONS= 1
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE

3. COEF INCREASE DECREASE
X1 1.000000 2.000000 INFINITY
X2 2.000000 4.000000 INFINITY
X3 3.000000 INFINITY 1.000000
X4 4.000000 2.000000 INFINITY
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
2 12.000000 INFINITY 12.000000
3 6.000000 INFINITY 6.000000
4 4.000000 INFINITY 4.000000
PREGUNTA 5
LP OPTIMUM FOUND AT STEP 2
OBJECTIVE FUNCTION VALUE
1) 25.00000
VARIABLE VALUE REDUCED COST
X1 15.000000 0.000000
X2 5.000000 0.000000
X3 0.000000 1.500000
ROW SLACK OR SURPLUS DUAL PRICES
2) 10.000000 0.000000
3) 0.000000 1.500000
4) 0.000000 0.500000
NO. ITERATIONS= 2
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X1 2.000000 INFINITY 1.000000
X2 -1.000000 1.000000 1.000000
X3 1.000000 1.500000 INFINITY
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
2 60.000000 INFINITY 10.000000
3 10.000000 10.000000 30.000000

4. 4 20.000000 5.000000 10.000000
PREGUNTA 6
LP OPTIMUM FOUND AT STEP 2
OBJECTIVE FUNCTION VALUE
1) 445000.0
VARIABLE VALUE REDUCED COST
X1 10000.000000 0.000000
X2 12500.000000 0.000000
X3 0.000000 21.799999
ROW SLACK OR SURPLUS DUAL PRICES
2) 75.000000 0.000000
3) 0.000000 35.000000
4) 0.000000 250.000000
5) 4500.000000 0.000000
NO. ITERATIONS= 2
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X1 16.000000 12.500000 1.750000
X2 22.799999 2.800000 10.000000
X3 12.400000 21.799999 INFINITY
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
2 1200.000000 INFINITY 75.000000
3 2000.000000 200.000000 500.000000
4 1500.000000 300.000000 180.000000
5 8000.000000 4500.000000 INFINITY
PREGUNTA 7
LP OPTIMUM FOUND AT STEP 2
OBJECTIVE FUNCTION VALUE

5. 1) 11.00000
VARIABLE VALUE REDUCED COST
X1 4.000000 0.000000
X2 5.000000 0.000000
X3 0.000000 2.400000
ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 0.200000
3) 0.000000 0.800000
4) 11.000000 0.000000
NO. ITERATIONS= 2
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X1 -1.000000 INFINITY 0.500000
X2 3.000000 INFINITY 1.000000
X3 -2.000000 2.400000 INFINITY
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
2 7.000000 INFINITY 10.000000
3 12.000000 22.000000 16.666666
4 10.000000 INFINITY 11.000000
PREGUNTA 8
LP OPTIMUM FOUND AT STEP 3
OBJECTIVE FUNCTION VALUE
1) 131.0000
VARIABLE VALUE REDUCED COST
X1 2.000000 0.000000
X2 30.000000 0.000000
X3 1.000000 0.000000
ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 0.857143
3) 0.000000 2.428571

6. 4) 0.000000 0.714286
NO. ITERATIONS= 3
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X1 4.000000 8.500000 5.000000
X2 4.000000 INFINITY 3.000000
X3 3.000000 3.000000 5.666667
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
2 10.000000 3.500000 13.999999
3 31.000000 7.000000 2.333333
4 66.000000 7.000000 13.999999
PREGUNTA 9
LP OPTIMUM FOUND AT STEP 2
OBJECTIVE FUNCTION VALUE
1) 76.66666
VARIABLE VALUE REDUCED COST
X1 0.000000 1.833333
X2 6.666667 0.000000
X3 16.666666 0.000000
ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 0.833333
3) 0.000000 0.666667
4) 26.666666 0.000000
NO. ITERATIONS= 2
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X1 2.000000 1.833333 INFINITY

7. X2 4.000000 2.000000 2.500000
X3 3.000000 5.000000 1.000000
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
2 60.000000 39.999996 19.999998
3 40.000000 19.999998 24.999998
4 80.000000 INFINITY 26.666666
PREGUNTA 10
LP OPTIMUM FOUND AT STEP 1
OBJECTIVE FUNCTION VALUE
1) 1200.000
VARIABLE VALUE REDUCED COST
X1 0.000000 0.740000
X2 800.000000 0.000000
ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 150.000000
3) 200.000000 0.000000
4) 400.000000 0.000000
NO. ITERATIONS= 1
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X1 0.010000 0.740000 INFINITY
X2 1.500000 INFINITY 1.480000
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
2 8.000000 2.000000 4.000000
3 1000.000000 INFINITY 200.000000
4 400.000000 400.000000 INFINITY
PREGUNTA 11