Variable Value Reduced Cost

MIN = @SUM(PARTS(I): OUTCOST(I)*BUY(I)+INCOST(I)*PRODUCE(I));

!Minimizing costs=sum of buying costs and production costs;

@FOR(PARTS(I):BUY(I)+PRODUCE(I)=6100);

!Sum of amount bought+amount produced of each part has to equal 6100;

@SUM(PARTS(I):CUTTIME(I)*PRODUCE(I))<=820;

@SUM(PARTS(I):SHAPETIME(I)*PRODUCE(I))<=820;

@SUM(PARTS(I):FABTIME(I)*PRODUCE(I))<=820;

!Sum of times has to be less than the total hour capacity of the department

that does that job.;

@FOR(PARTS(I):@GIN(BUY(I)));

FOR(PARTS(I):@GIN(PRODUCE(I)));

END

Global optimal solution found.

Objective value: 29256.40

Objective bound: 29256.40

Infeasibilities: 0.000000

Extended solver steps: 0

Total solver iterations: 3

Variable Value Reduced Cost

OUTCOST( SHAFT) 1.210000 0.000000

OUTCOST( BASE) 2.500000 0.000000

OUTCOST( CAGE) 1.950000 0.000000

INCOST( SHAFT) 0.8100000 0.000000

INCOST( BASE) 2.300000 0.000000

INCOST( CAGE) 1.450000 0.000000

BUY( SHAFT) 0.000000 1.210000

BUY( BASE) 2642.000 2.500000

BUY( CAGE) 1824.000 1.950000

PRODUCE( SHAFT) 6100.000 0.8100000

PRODUCE( BASE) 3458.000 2.300000

PRODUCE( CAGE) 4276.000 1.450000

CUTTIME( SHAFT) 0.4000000E-01 0.000000

CUTTIME( BASE) 0.8000000E-01 0.000000

CUTTIME( CAGE) 0.7000000E-01 0.000000

SHAPETIME( SHAFT) 0.6000000E-01 0.000000

SHAPETIME( BASE) 0.2000000E-01 0.000000

SHAPETIME( CAGE) 0.9000000E-01 0.000000

FABTIME( SHAFT) 0.4000000E-01 0.000000

FABTIME( BASE) 0.5000000E-01 0.000000

FABTIME( CAGE) 0.6000000E-01 0.000000

CAPACITY( CUTTING) 820.0000 0.000000

CAPACITY( SHAPING) 820.0000 0.000000

CAPACITY( FABRICATION) 820.0000 0.000000

Row Slack or Surplus Dual Price

1 29256.40 -1.000000

2 0.000000 0.000000

3 0.000000 0.000000

4 0.000000 0.000000

5 0.4000000E-01 0.000000

6 0.000000 0.000000

7 146.5400 0.000000

3. The following math model can be converted to LINGO:

LINGO Model:

Model:

SETS:

PROFS: TOTTEACH, FTEACH, STEACH, SATEACH, SBTEACH, FATEACH, FBTEACH, ABID,

BBID, MAXS, MAXF;

!TOTTEACH=The total number of courses that must be taught by the professor.

FTEACH=The # of courses the prof teaches in the fall.

STEACH=The # of courses the prof teaches in the spring.

SATEACH=The # of course A the prof teaches in the spring.

SBTEACH=The # of course B the prof teaches in the spring.

FATEACH, F_B_TEACH=Similar to above, but in the fall.

ABID, BBID= The bids for courses A and B the prof has given.

MAXS=The max number of courses the professor wishes to teach in the spring.

MAXF=The max number of courses the prof wishes to teach in the fall.;

COURSES: MINI, MAXI, TOTAL;

!MINI=The minimum # of sections of the course required.

MAXI=The maximum # of sections of the course required.

TOTAL=The total # of sections of the course offered.;