8.1
Page 1
Linear, Integer and Mixed Integer Programming
Signs
<
less than or equal to
=
equals (You need to enter an apostrophe first.)
>
greater than or equal to
Data
X 1
X 2
Objective
28
25
Constraint 1
3
2
Constraint 2
1.5
1
Constraint 3
0.75
0.75
Constraint 4
1
1
Results
Variables
26.666667
140
Objective
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
To use Integer variables, define them in the Solver model as a constraint.
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
8.1
Page 2
less than or equal to
equals (You need to enter an apostrophe first.)
greater than or equal to
Results
LHS
Slack/Surplus
sign
RHS
4246.6667
<
360
360
0
<
200
180
20
<
125
125
0
>
60
166.66667 -106.66667
4246.6667
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
To use Integer variables, define them in the Solver model as a constraint.
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
8-2
Page 3
Linear, Integer and Mixed Integer Programming
Signs
<
=
>
Data
X 1
X 2
Objective
0.053
0.068
Constraint 1
1
1
Constraint 2
0.8
-0.2
Constraint 3
-0.4
0.6
Constraint 4
-0.5
0
Results
Variables
50000
0
Objective
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
To use Integer variables, define them in the Solver model as a constraint.
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
8-2
Page 4
less than or equal to
equals (You need to enter an apostrophe first.)
greater than or equal to
Results
X 3
X 4
X 5
LHS
Slack/Surplus
0.049
0.084
0.118 sign
RHS
20300
1
1
1 <
250000
250000
0
-0.2
-0.2
-0.2 >
0
0
0
0.6
0.6
-0.4 >
0
75000
-75000
0
0
1 <
0
0
0
0
175000
25000
20300
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
To use Integer variables, define them in the Solver model as a constraint.
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
8-10
Page 5
Linear, Integer and Mixed Integer Programming
Signs
<
=
>
Data
X 1
X 2
Objective
1
1
Constraint 1
5
Constraint 2
8
4
Constraint 3
6
12
Constraint 4
1
1
Results
Variables
95.294118
0
Objective
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
To use Integer variables, define them in the Solver model as a constraint.
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
8-10
Page 6
less than or equal to
equals (You need to enter an apostrophe first.)
greater than or equal to
Results
X 3
X 4
X 5
LHS
Slack/Surplus
1
1
sign
RHS
142.18487
4
7
12 <
900
900
0
2
7 <
900
900
0
7
5
<
900
900
0
1
1
1 =
2500
161.84874 2338.1513
46.890756
0 19.663866
142.18487
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
To use Integer variables, define them in the Solver model as a constraint.
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
8-10.2
Page 7
Linear, Integer and Mixed Integer Programming
Signs
<
less than or equal to
=
equals (You need to enter an apostrophe first.)
>
greater than or equal to
Data
Results
X 1
X 2
X 3
X 4
X 5
LHS
Objective
1
1
1
1
1 sign
RHS
161.84874
Constraint 1
5
0
4
7
12 <
900
900
Constraint 2
8
4
0
2
7 <
900
900
Constraint 3
6
12
7
5
0 <
900
900
Constraint 4
1
1
1
1
1 =
2500
161.84874
Results
Variables
95.294118
0 46.890756
0 19.663866
Objective
161.84874
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
To use Integer variables, define them in the Solver model as a constraint.
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
8-10.2
Page 8
Slack/Surplus
0
0
0
2338.1513
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
To use Integer variables, define them in the Solver model as a constraint.
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
8-10.solve
Page 9
Linear, Integer and Mixed Integer Programming
Signs
<
=
>
Data
X 1
X 2
Objective
5
8
Constraint 1
1
1
Constraint 2
Constraint 3
Constraint 4
Constraint 5
Constraint 6
1
Constraint 7
1
Constraint 8
Results
Variables
0
700
Objective
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
To use Integer variables, define them in the Solver model as a constraint.
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
8-10.solve
Page 10
X 3
X 4
X 5
X 6
X 7
X 8
X 9
X 10
X 11
X 12
X 13
6
0
4
12
4
0
7
7
2
5
12
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
500
0
0
100
500
0
300
400
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
To use Integer variables, define them in the Solver model as a constraint.
Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE. If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.
