GAMS 2.25.089 DEC AXP/UNIX 09/17/03 16:43:55 PAGE 1 G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m C o m p i l a t i o n 1 set x inputs /bread, meat, milk/ 2 z outputs /meal1, meal2, meal3/; 3 4 alias (x,xx); 5 alias (z,zz); 6 7 table aa(x,xx) quadratic price coefficients 8 bread meat milk 9 bread -0.01 0.003 0.002 10 meat 0.003 -0.05 0.001 11 milk 0.002 0.001 -0.07 12 13 table bb(z,zz) quadratic quantity coefficients 14 meal1 meal2 meal3 15 meal1 0.050 0.000 -0.003 16 meal2 0.000 0.060 -0.002 17 meal3 -0.003 -0.002 0.075 18 19 table gg(x,z) effect of quantity on price 20 meal1 meal2 meal3 21 bread 0.003 0.000 0.000 22 meat 0.000 0.004 0.000 23 milk 0.000 0.000 0.005 24 25 parameter a(x) price constants 26 /bread 100, 27 meat 50, 28 milk 75/; 29 30 parameter b(z) quantity coefficients 31 /meal1 0, 32 meal2 0, 33 meal3 0/; 34 35 parameter ps(x) prices 36 /bread 1.00, 37 meat 4.00, 38 milk 1.89/; 39 40 variables p(x) input prices 41 q(z) output levels 42 u utility; 43 44 positive variable q(z); 45 46 equations cost household cost function 47 utility utility function; 48 49 cost.. sum(x,a(x)*p(x)+sum(xx,p(x)*aa(x,xx)*p(xx)))+sum(z,b(z)*q(z) +sum(zz,q(z)*bb(z,zz)*q(zz)))+ 50 sum((x,z),p(x)*q(z)*gg(x,z)) =l= 450.0; 51 utility.. q("meal1")**.3*q("meal2")**.4*q("meal3")**.3 =e= u; 52 53 q.lo(z) = 0.001; 54 p.fx(x) = ps(x); 55 56 model port using /all/; 57 solve port using nlp maximizing u; 58 59 GAMS 2.25.089 DEC AXP/UNIX 09/17/03 16:43:55 PAGE 2 G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m Symbol Listing SYMBOL TYPE REFERENCES A PARAM DECLARED 25 DEFINED 26 REF 49 AA PARAM DECLARED 7 DEFINED 7 REF 49 B PARAM DECLARED 30 DEFINED 31 REF 49 BB PARAM DECLARED 13 DEFINED 13 REF 49 COST EQU DECLARED 46 DEFINED 49 IMPL-ASN 57 REF 56 GG PARAM DECLARED 19 DEFINED 19 REF 50 P VAR DECLARED 40 IMPL-ASN 57 ASSIGNED 54 REF 3*49 50 PORT MODEL DECLARED 56 DEFINED 56 IMPL-ASN 57 REF 57 PS PARAM DECLARED 35 DEFINED 36 REF 54 Q VAR DECLARED 41 IMPL-ASN 57 ASSIGNED 53 REF 44 3*49 50 3*51 U VAR DECLARED 42 IMPL-ASN 57 REF 51 57 UTILITY EQU DECLARED 47 DEFINED 51 IMPL-ASN 57 REF 56 X SET DECLARED 1 DEFINED 1 REF 4 7 19 25 35 40 4*49 2*50 54 CONTROL 49 50 54 XX SET DECLARED 4 REF 7 2*49 CONTROL 49 Z SET DECLARED 2 DEFINED 2 REF 5 13 19 30 41 44 4*49 2*50 CONTROL 49 50 53 ZZ SET DECLARED 5 REF 13 2*49 CONTROL 49 SETS X inputs XX Aliased with X Z outputs ZZ Aliased with Z PARAMETERS A price constants AA quadratic price coefficients B quantity coefficients BB quadratic quantity coefficients GG effect of quantity on price PS prices VARIABLES P input prices Q output levels U utility EQUATIONS COST household cost function UTILITY utility function GAMS 2.25.089 DEC AXP/UNIX 09/17/03 16:43:55 PAGE 3 G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m Symbol Listing MODELS PORT using COMPILATION TIME = 0.033 SECONDS VERID AXU-25-089 GAMS 2.25.089 DEC AXP/UNIX 09/17/03 16:43:55 PAGE 4 G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m Equation Listing SOLVE PORT USING NLP FROM LINE 57 ---- COST =L= household cost function COST.. (100.0116)*P(BREAD) + (49.6098)*P(MEAT) + (74.7474)*P(MILK) + (0.0031)*Q(MEAL1) + (0.0161)*Q(MEAL2) + (0.0096)*Q(MEAL3) =L= 450 ; (LHS = 440.7367) ---- UTILITY =E= utility function UTILITY.. (0.3)*Q(MEAL1) + (0.4)*Q(MEAL2) + (0.3)*Q(MEAL3) - U =E= 0 ; (LHS = 0.001 ***) GAMS 2.25.089 DEC AXP/UNIX 09/17/03 16:43:55 PAGE 5 G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m Column Listing SOLVE PORT USING NLP FROM LINE 57 ---- P input prices P(BREAD) (.LO, .L, .UP = 1, 1, 1) (100.0116) COST 0 (DUAL) P(MEAT) (.LO, .L, .UP = 4, 4, 4) (49.6098) COST 0 (DUAL) P(MILK) (.LO, .L, .UP = 1.89, 1.89, 1.89) (74.7474) COST 0 (DUAL) ---- Q output levels Q(MEAL1) (.LO, .L, .UP = 0.001, 0.001, +INF) (0.0031) COST (0.3) UTILITY 0 (DUAL) Q(MEAL2) (.LO, .L, .UP = 0.001, 0.001, +INF) (0.0161) COST (0.4) UTILITY 0 (DUAL) Q(MEAL3) (.LO, .L, .UP = 0.001, 0.001, +INF) (0.0096) COST (0.3) UTILITY 0 (DUAL) ---- U utility U (.LO, .L, .UP = -INF, 0, +INF) -1 UTILITY 0 (OBJECTIVE) GAMS 2.25.089 DEC AXP/UNIX 09/17/03 16:43:55 PAGE 6 G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m Model Statistics SOLVE PORT USING NLP FROM LINE 57 MODEL STATISTICS BLOCKS OF EQUATIONS 2 SINGLE EQUATIONS 2 BLOCKS OF VARIABLES 3 SINGLE VARIABLES 7 NON ZERO ELEMENTS 10 NON LINEAR N-Z 9 DERIVATIVE POOL 15 CONSTANT POOL 26 CODE LENGTH 394 GENERATION TIME = 0.033 SECONDS EXECUTION TIME = 0.033 SECONDS VERID AXU-25-089 GAMS 2.25.089 DEC AXP/UNIX 09/17/03 16:43:55 PAGE 7 G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m Solution Report SOLVE PORT USING NLP FROM LINE 57 S O L V E S U M M A R Y MODEL PORT OBJECTIVE U TYPE NLP DIRECTION MAXIMIZE SOLVER MINOS5 FROM LINE 57 **** SOLVER STATUS 1 NORMAL COMPLETION **** MODEL STATUS 2 LOCALLY OPTIMAL **** OBJECTIVE VALUE 7.2692 RESOURCE USAGE, LIMIT 0.201 1000.000 ITERATION COUNT, LIMIT 28 1000 EVALUATION ERRORS 0 0 GAMS/MINOS 5.4 Aug 1, 1996 002.103.030-033.030 AXP/OSF B. A. Murtagh, University of New South Wales and P. E. Gill, W. Murray, M. A. Saunders and M. H. Wright Systems Optimization Laboratory, Stanford University. Work space allocated -- 0.04 Mb EXIT -- OPTIMAL SOLUTION FOUND MAJOR ITNS, LIMIT 8 200 FUNOBJ, FUNCON CALLS 65 65 SUPERBASICS 2 INTERPRETER USAGE 0.01 NORM RG / NORM PI 1.325E-07 LOWER LEVEL UPPER MARGINAL ---- EQU COST -INF 450.000 450.000 0.397 ---- EQU UTILITY . . . -1.000 COST household cost function UTILITY utility function ---- VAR P input prices LOWER LEVEL UPPER MARGINAL BREAD 1.000 1.000 1.000 -39.695 MEAT 4.000 4.000 4.000 -19.698 MILK 1.890 1.890 1.890 -29.673 ---- VAR Q output levels LOWER LEVEL UPPER MARGINAL MEAL1 0.001 7.589 +INF EPS MEAL2 0.001 7.852 +INF . MEAL3 0.001 6.282 +INF EPS GAMS 2.25.089 DEC AXP/UNIX 09/17/03 16:43:55 PAGE 8 G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m Solution Report SOLVE PORT USING NLP FROM LINE 57 LOWER LEVEL UPPER MARGINAL ---- VAR U -INF 7.269 +INF . U utility **** REPORT SUMMARY : 0 NONOPT 0 INFEASIBLE 0 UNBOUNDED 0 ERRORS EXECUTION TIME = 0.017 SECONDS VERID AXU-25-089 USER: Charles Moss G961213:1904AP-AXU University of Florida **** FILE SUMMARY INPUT /usr/users/chuck/hpm.gms OUTPUT /usr/users/chuck/hpm.lst