* GAMS Solution to PS06_2
* 28 October, 2006

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option
        limrow=0
        limcol=0                ;

variables
        x1
        x2
        x3
        x4
        x5
        F                                               ;

positive variables x1
                   x2                                   ;

integer variables  x4
                   x5                                   ;

* initialize variables for non-linear solver

x1.l = 4                                                ;
x2.l = 4                                                ;
x3.l = 4                                                ;

equations
        obj1    'objective function 1'
        obj2    'objective function 2'
        obj3    'objective function 3'
        obj4    'objective function 4'
        cnst1   'constraint 1'
        cnst2   'constraint 2'
        cnst3   'constraint 3'
        cnst4   'constraint 4'
        cnst5   'constraint 5'
        cnst6   'constraint 6'
        cnst7   'constraint 7'
        cnst8   'constraint 8'
        cnst9   'constraint 9'                          ;

obj1..    F =e= (-sqr(x1) - sqr(x2))                    ;
obj2..    F =e= -sqr(x1 - 1) - 2*sqr(x2) - sqr(x3)      ;
obj3..    F =e= x1 + (2*x2)                             ;
obj4..    F =e= 3*x4 - 7*x5                             ;
cnst1..   -(x1*x2) =l= -1                               ;
cnst2..   (-3*x1) - x2 =l= -2                           ;
cnst3..   -x2 =l= -0.2                                  ;
cnst4..   2*sqrt(x1) - x3 =e= 0                                ;
cnst5..   -2*x1 - x2 =l= -2                             ;
cnst6..   -x1 + (2*x2)  =l= 2                           ;
cnst7..   x1 + x2 =l= 1                                        ;
cnst8..          -x4 + x5 =l= 0                                ;
cnst9..          x4 + x5 =l= 3.5                                ;

model prob1 /obj1, cnst1 /                              ;
model prob2 /obj1, cnst2, cnst3 /                       ;
model prob3 /obj2, cnst4, cnst5 /                       ;
model prob4 /obj3, cnst6, cnst7 /                       ;
model prob5 /obj4, cnst8, cnst9 /                       ;

solve prob1 using nlp maximizing  F                     ;
        file results /PS06_2.res/                      ;
        put results                                     ;
        put 'GAMS RESULTS'///        ;
        put 'Problem 1'/                                ;
        put @5, 'F', @15, F.l /                                ;
        put @5, 'x1', @15, x1.l /                       ;
        put @5, 'x2', @15, x2.l ///                     ;
solve prob2 using nlp maximizing  F                     ;
        put 'Problem 2' /                               ;
        put @5, 'F', @15, F.l /                                ;
        put @5, 'x1', @15, x1.l /                       ;
        put @5, 'x2', @15, x2.l ///                     ;
solve prob3 using nlp maximizing  F                     ;
        put 'Problem 3' /                               ;
        put @5, 'F', @15, F.l /                                ;
        put @5, 'x1', @15, x1.l /                       ;
        put @5, 'x2', @15, x2.l /                       ;
        put @5, 'x3', @15, x3.l ///                     ;
solve prob4 using lp  maximizing  F                     ;
        put 'Problem 4' /                               ;
        put @5, 'F', @15, F.l /                                ;
        put @5, 'x1', @15, x1.l /                       ;
        put @5, 'x2', @15, x2.l ///                     ;
solve prob5 using mip maximizing  F                     ;
        put 'Problem 5' /                               ;
        put @5, 'F', @15, F.l /                                ;
        put @5, 'x', @15, x4.l /                        ;
        put @5, 'y', @15, x5.l ///                      ;
putclose results                                        ;