Linear Programing

8.1

Enter Enter the the values values in in the the shaded shaded ar a IfIf SOLVER SOLVER isis not not on on the the Data Data Tab Tab To Touse use Integer Integer variables, variables, define define th t

Linear, Integer and Mixed Integer Programming Signs < = >

less than or equal to equals (You need to enter an apos greater than or equal to

Data X1 Objective Constraint Constraint Constraint Constraint

1 2 3 4

Results Variables Objective

Page 1

X2 28 3 1.5 0.75 1

25 2 1 0.75 1

26.666667

140

8.1

Enter Enter the the values values in in the the shaded shaded area. area. Then Then go go to to the the DATA DATATab Tab on on the the ribbon, ribbon, click click on on Solver Solver in in the the Data DataAnalysis Analysis Group Group and and then then click click SOLVE. SOLVE. IfIf SOLVER SOLVER isis not not on on the the Data Data Tab Tab then then please please see see the the Help Help file file (Solver) (Solver) for for instructions. instructions. To Touse use Integer Integer variables, variables, define define them them in in the the Solver Solver model model as as aa constraint. constraint.

ess than or equal to quals (You need to enter an apostrophe first.) reater than or equal to

sign < < < >

RHS 360 200 125 60

Results LHS Slack/Surplus 4246.6667 360 0 180 20 125 0 166.66667 -106.66667

4246.6667

Page 2

8-2

Enter Enter the the values values in in the the shaded shaded ar a IfIf SOLVER SOLVER isis not not on on the the Data Data Tab Tab To Touse use Integer Integer variables, variables, define define th t

Linear, Integer and Mixed Integer Programming Signs < = > Data X1 Objective Constraint Constraint Constraint Constraint

1 2 3 4

Results Variables Objective

Page 3

X2 0.053 1 0.8 -0.4 -0.5

0.068 1 -0.2 0.6 0

50000

0

8-2

Enter Enter the the values values in in the the shaded shaded area. area. Then Then go go to to the the DATA DATATab Tab on on the the ribbon, ribbon, click click on on Solver Solver in in the the Data DataAnalysis Analysis Group Group and and then then click click SOLVE. SOLVE. IfIf SOLVER SOLVER isis not not on on the the Data Data Tab Tab then then please please see see the the Help Help file file (Solver) (Solver) for for instructions. instructions. To Touse use Integer Integer variables, variables, define define them them in in the the Solver Solver model model as as aa constraint. constraint.

less than or equal to equals (You need to enter an apostrophe first.) greater than or equal to

X3

X4

Results LHS Slack/Surplus 20300 250000 0 0 0 75000 -75000 0 0

X5

0.049 1 -0.2 0.6 0

0.084 1 -0.2 0.6 0

0

175000

0.118 sign 1< -0.2 > -0.4 > 1<

RHS 250000 0 0 0

25000 20300

Page 4

8-10

Enter Enter the the values values in in the the shaded shaded ar a IfIf SOLVER SOLVER isis not not on on the the Data Data Tab Tab To Touse use Integer Integer variables, variables, define define th t

Linear, Integer and Mixed Integer Programming Signs < = > Data X1 Objective Constraint Constraint Constraint Constraint

1 2 3 4

Results Variables Objective

Page 5

X2 1 5 8 6 1

1 4 12 1

95.294118

0

8-10

Enter Enter the the values values in in the the shaded shaded area. area. Then Then go go to to the the DATA DATATab Tab on on the the ribbon, ribbon, click click on on Solver Solver in in the the Data DataAnalysis Analysis Group Group and and then then click click SOLVE. SOLVE. IfIf SOLVER SOLVER isis not not on on the the Data Data Tab Tab then then please please see see the the Help Help file file (Solver) (Solver) for for instructions. instructions. To Touse use Integer Integer variables, variables, define define them them in in the the Solver Solver model model as as aa constraint. constraint.

less than or equal to equals (You need to enter an apostrophe first.) greater than or equal to

X3

X4 1 4 7 1

46.890756

Results LHS Slack/Surplus 142.18487 900 0 900 0 900 0 161.84874 2338.1513

X5 1 7 2 5 1

sign 12 < 7< < 1=

RHS 900 900 900 2500

0 19.663866 142.18487

Page 6

8-10.2

Enter in Linear, Integer and Mixed Integer Programming Enter the the values values in the the shaded shaded area. area. Then Then go go to to the the DATA DATATab Tab on on the the ribbon, ribbon, click click on on Solver Solver in in the the Data DataAnalysis Analysis Group Group and and then then clic clic IfIf SOLVER SOLVER isis not not on on the the Data Data Tab Tab then then please please see see the the Help Help file file (Solver) (Solver) for for instructions. instructions. To Touse use Integer Integer variables, variables, define define them them in in the the Solver Solver model model as as aa constraint. constraint.

Signs < = >

less than or equal to equals (You need to enter an apostrophe first.) greater than or equal to

Data X1 Objective Constraint Constraint Constraint Constraint Results Variables Objective

1 2 3 4

X2 1 5 8 6 1

95.294118

X3 1 0 4 12 1

X4 1 4 0 7 1

0 46.890756

X5 1 7 2 5 1

1 sign 12 < 7< 0< 1=

RHS 900 900 900 2500

0 19.663866 161.84874

Page 7

Results LHS 161.84874 900 900 900 161.84874

8-10.2

ata ataAnalysis Analysis Group Group and and then then click click SOLVE. SOLVE.

Slack/Surplus 0 0 0 2338.1513

Page 8

8-10.solve

Enter Enter the the values values in in the the shaded shaded ar a IfIf SOLVER SOLVER isis not not on on the the Data Data Tab Ta To Touse use Integer Integer variables, variables, define define th t

Linear, Integer and Mixed Integer Programming Signs < = > Data X1 Objective Constraint Constraint Constraint Constraint Constraint Constraint Constraint Constraint

X2 5 1

1 2 3 4 5 6 7 8

8 1

1 1

Results Variables Objective

0

Page 9

700

8-10.solve

Enter Enter the the values values in in the the shaded shaded area. area. Then Then go go to to the the DATA DATATab Tab on on the the ribbon, ribbon, click click on on Solver Solver in in the the Data DataAnalysis Analysis Group Group and and then then click click SOLVE. SOLVE. IfIf SOLVER SOLVER isis not not on on the the Data Data Tab Tab then then please please see see the the Help Help file file (Solver) (Solver) for for instructions. instructions. To Touse use Integer Integer variables, variables, define define them them in in the the Solver Solver model model as as aa constraint. constraint.

X3

X4 6 1

X5 0

X6

X7

4

12

1

1

X8

X9

4

0

1

X 10 7

X 11

5

1

1

1

1 1

0

0

12

1 1

1

1

0

X 13

2

1

1 1

X 12

7

500

1

0

0

Page 10

100

1

500

0

300

400

8-10.solve

less than or equal to equals (You need to enter an apostrophe first.) greater than or equal to

X 14

X 15 7

1 1

0

0 sign = = = = = < < <

RHS 700 500 100 800 400 900 900 900

Results LHS Slack/Surplus 22100 700 0 500 0 100 0 800 0 400 0 900 0 700 200 900 0

0 22100

Page 11