ST
x11+x12+x13+x14+s1=1000
x21+x22+x23+x24+s2=1000
x31+x32+x33+x34+s3=1500
x11+x21+x31=500
x12+x22+x32=700
x13+x23+x33=600
x14+x24+x34=800
LINDO:
LP OPTIMUM FOUND AT STEP 14
OBJECTIVE FUNCTION VALUE
1) 22900.00
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 300.000000 0.000000
X24 0.000000 1.000000
X31 500.000000 0.000000
X32 0.000000 2.000000
X33 0.000000 0.000000
X34 800.000000 0.000000
S1 0.000000 3.000000
S2 700.000000 0.000000
S3 200.000000 0.000000
ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 -1.000000
3) 0.000000 -4.000000
4) 0.000000 -4.000000
5) 0.000000 20.000000
6) 0.000000 13.000000
7) 0.000000 10.000000
8) 0.000000 11.000000
NO. ITERATIONS= 14
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X11 15.000000 4.000000 INFINITY
X12 12.000000 INFINITY 2.000000
X13 9.000000 2.000000 3.000000
X14 2.000000 8.000000 INFINITY
X21 3.000000 13.000000 INFINITY
X22 7.000000 2.000000 INFINITY
X23 6.000000 3.000000 0.000000
X24 6.000000 1.000000 INFINITY
X31 16.000000 INFINITY 4.000000
X32 7.000000 2.000000 INFINITY
X33 6.000000 0.000000 INFINITY
X34 7.000000 INFINITY 1.000000
S1 -4.000000 3.000000 INFINITY
S2 -4.000000 0.000000 1.000000
S3 -4.000000 1.000000 0.000000
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
2 1000.000000 300.000000 300.000000
3 1000.000000 INFINITY 700.000000
4 1500.000000 INFINITY 200.000000
5 500.000000 200.000000 500.000000
6 700.000000 300.000000 300.000000
7 600.000000 700.000000 300.000000
8 800.000000 200.000000 800.000000
min 12x11+15x12+16x13+14x14+15x21+2x22+18x23+16x24+10x31+15x32+8x33+6x34+2000dt1+25000dt2+20000dt3+15000dt4
ST
x11+x12+x13+x14=150
x21+x22+x23+x24=100
x31+x32+x33+x34=50
x11+x21+x31+dt1=100
x12+x22+x32+dt2=75
x13+x23+x33+dt3=50
x14+x24+x34+dt4=125
LINDO:
LP OPTIMUM FOUND AT STEP 5
OBJECTIVE FUNCTION VALUE
1) 102950.0
VARIABLE VALUE REDUCED COST
X11 50.000000 0.000000
X12 0.000000 15.000000
X13 50.000000 0.000000
X14 50.000000 0.000000
X21 0.000000 1.000000
X22 75.000000 0.000000
X23 0.000000 0.000000
X24 25.000000 0.000000
X31 0.000000 6.000000
X32 0.000000 23.000000
X33 0.000000 0.000000
X34 50.000000 0.000000
DT1 50.000000 0.000000
DT2 0.000000 23012.000000
DT3 0.000000 17996.000000
DT4 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= 5
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 INFINITY
X14 14.000000 15.000000 0.000000
X21 15.000000 INFINITY 1.000000
X22 2.000000 15.000000 INFINITY
X23 18.000000 INFINITY 0.000000
X24 16.000000 0.000000 15.000000
X31 10.000000 INFINITY 6.000000
X32 15.000000 INFINITY 23.000000
X33 8.000000 INFINITY 0.000000
X34 6.000000 0.000000 INFINITY
DT1 2000.000000 12998.000000 INFINITY
DT2 25000.000000 INFINITY 23012.000000
DT3 20000.000000 INFINITY 17996.000000
DT4 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 50.000000 25.000000
4 50.000000 50.000000 50.000000
5 100.000000 INFINITY 50.000000
6 75.000000 25.000000 50.000000
7 50.000000 50.000000 50.000000
8 125.000000 50.000000 50.000000
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