Una empresa suministra patatas a cuatro mayoristas cuyas demandas respectivamante son 100,75,50,125.dispone de tres almacenes, en diferentes puntos, cuyas capacidades son 150,100 y 50 toneladas. Si los costos de distribución, en miles de pesetas por tonelada, de cada almacén a cada mayorista son:
| M1 | M2 | M3 | M4 | |
| A1 | 12 | 15 | 16 | 14 |
| A2 | 15 | 2 | 18 | 16 |
| A3 | 10 | 15 | 8 | 6 |
Formular un programa lineal que permita calcular la política de distribución óptima sabiendo quepor cada tonelada de demanda insatisfecha la empresa tiene unas pérdidas de 2000, 25000, 20000, 15000 pts. respectivamente.
Min
12x11+15x12+16x13+14x14+15x21+2x22+18x23+16x24+10x31+15x32+8x33+6x34+2000s1+25000s2+20000s3+15000s4
st
x11+x12+x13+x14=150
x21+x22+x23+x24=100
x31+x32+x33+x34=50
x11+x21+x31+s1=100
x12+x22+x32+s2=75
x13+x23+x33+s3=50
x14+x24+x34+s4=125
end
LP OPTIMUM FOUND AT STEP 6
OBJECTIVE FUNCTION VALUE
1) 30600.00
VARIABLE VALUE REDUCED COST
X11 0.000000 4.000000
X12 700.000000 0.000000
X13 300.000000 0.000000
X14 0.000000 8.000000
X21 0.000000 13.000000
X22 0.000000 2.000000
X23 100.000000 0.000000
X24 0.000000 1.000000
X31 500.000000 0.000000
X32 0.000000 2.000000
X33 200.000000 0.000000
X34 800.000000 0.000000
ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 3.000000
3) 900.000000 0.000000
4) 0.000000 0.000000
5) 0.000000 -9.000000
6) 0.000000 -17.000000
7) 0.000000 -14.000000
8) 0.000000 -11.000000
NO. ITERATIONS= 6
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X11 10.000000 INFINITY 4.000000
X12 14.000000 2.000000 INFINITY
X13 11.000000 3.000000 2.000000
X14 16.000000 INFINITY 8.000000
X21 22.000000 INFINITY 13.000000
X22 19.000000 INFINITY 2.000000
X23 14.000000 1.000000 0.000000
X24 12.000000 INFINITY 1.000000
X31 9.000000 4.000000 INFINITY
X32 19.000000 INFINITY 2.000000
X33 14.000000 0.000000 1.000000
X34 11.000000 1.000000 INFINITY
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
2 1000.000000 100.000000 300.000000
3 1000.000000 INFINITY 900.000000
4 1500.000000 100.000000 200.000000
5 500.000000 200.000000 100.000000
6 700.000000 300.000000 100.000000
7 600.000000 900.000000 100.000000
8 800.000000 200.000000 100.000000
LP OPTIMUM FOUND AT STEP 8
OBJECTIVE FUNCTION VALUE
1) 102950.0
VARIABLE VALUE REDUCED COST
X11 50.000000 0.000000
X12 0.000000 15.000000
X13 25.000000 0.000000
X14 75.000000 0.000000
X21 0.000000 1.000000
X22 75.000000 0.000000
X23 25.000000 0.000000
X24 0.000000 0.000000
X31 0.000000 6.000000
X32 0.000000 23.000000
X33 0.000000 0.000000
X34 50.000000 0.000000
S1 50.000000 0.000000
S2 0.000000 23012.000000
S3 0.000000 17996.000000
S4 0.000000 12998.000000
ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 1988.000000
3) 0.000000 1986.000000
4) 0.000000 1996.000000
5) 0.000000 -2000.000000
6) 0.000000 -1988.000000
7) 0.000000 -2004.000000
8) 0.000000 -2002.000000
NO. ITERATIONS= 8
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X11 12.000000 1.000000 12998.000000
X12 15.000000 INFINITY 15.000000
X13 16.000000 0.000000 0.000000
X14 14.000000 0.000000 0.000000
X21 15.000000 INFINITY 1.000000
X22 2.000000 15.000000 INFINITY
X23 18.000000 0.000000 15.000000
X24 16.000000 INFINITY 0.000000
X31 10.000000 INFINITY 6.000000
X32 15.000000 INFINITY 23.000000
X33 8.000000 INFINITY 0.000000
X34 6.000000 0.000000 INFINITY
S1 2000.000000 12998.000000 INFINITY
S2 25000.000000 INFINITY 23012.000000
S3 20000.000000 INFINITY 17996.000000
S4 15000.000000 INFINITY 12998.000000
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
2 150.000000 50.000000 50.000000
3 100.000000 25.000000 25.000000
4 50.000000 50.000000 50.000000
5 100.000000 INFINITY 50.000000
6 75.000000 25.000000 25.000000
7 50.000000 50.000000 25.000000
8 125.000000 50.000000 50.000000
LP OPTIMUM FOUND AT STEP 8
OBJECTIVE FUNCTION VALUE
1) 102950.0
VARIABLE VALUE REDUCED COST
X11 50.000000 0.000000
X12 0.000000 15.000000
X13 25.000000 0.000000
X14 75.000000 0.000000
X21 0.000000 1.000000
X22 75.000000 0.000000
X23 25.000000 0.000000
X24 0.000000 0.000000
X31 0.000000 6.000000
X32 0.000000 23.000000
X33 0.000000 0.000000
X34 50.000000 0.000000
S1 50.000000 0.000000
S2 0.000000 23012.000000
S3 0.000000 17996.000000
S4 0.000000 12998.000000
ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 1988.000000
3) 0.000000 1986.000000
4) 0.000000 1996.000000
5) 0.000000 -2000.000000
6) 0.000000 -1988.000000
7) 0.000000 -2004.000000
8) 0.000000 -2002.000000
NO. ITERATIONS= 8
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X11 12.000000 1.000000 12998.000000
X12 15.000000 INFINITY 15.000000
X13 16.000000 0.000000 0.000000
X14 14.000000 0.000000 0.000000
X21 15.000000 INFINITY 1.000000
X22 2.000000 15.000000 INFINITY
X23 18.000000 0.000000 15.000000
X24 16.000000 INFINITY 0.000000
X31 10.000000 INFINITY 6.000000
X32 15.000000 INFINITY 23.000000
X33 8.000000 INFINITY 0.000000
X34 6.000000 0.000000 INFINITY
S1 2000.000000 12998.000000 INFINITY
S2 25000.000000 INFINITY 23012.000000
S3 20000.000000 INFINITY 17996.000000
S4 15000.000000 INFINITY 12998.000000
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
2 150.000000 50.000000 50.000000
3 100.000000 25.000000 25.000000
4 50.000000 50.000000 50.000000
5 100.000000 INFINITY 50.000000
6 75.000000 25.000000 25.000000
7 50.000000 50.000000 25.000000
8 125.000000 50.000000 50.000000
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