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$Exercice 1$
Variables
positive variable X1;
negative variable X3;
free variable X2,Z;
Equations
con1,
con2,
con3,
objet;
con1 . . X1+X2+X3 = L = 7;
con2 . . 4*X1+2*X2 = E = 4;
con3 . . 10*X1 + X3 = G = 30;
obj . . 30*X1 + 100*X2 - 50*X3 = E = Z;
Model mesa / all/;
options LP = Cplex;
solve mesa using LP;
********EXERCICE 2***********************
positive Variables X1,X2;
Free Variable U;
Equations
con,
obj;
con .. 10*X1+80*X2=E=2400;
obj .. X1*X2=E=U;
Model meso /all/;
solve meso using NLP maximising U;
display X1.L,X2.L,U.L;
******Exercice 3**************
positive Variables Q1,Q2;
Free Variable i;
Equations
con1,
con2,
con3,
con4,
obj;
con1 .. Q1+Q2=L=200;
con2 .. 2*Q1+8*Q2=L=1000;
con3 .. Q1=G=50;
con4 .. Q2=G=30;
obj .. 2*Q1+3*Q2=E=i;

Model Exo /all/;
solve Exo using LP maximising i;
display Q1.L,Q2.L,i.L;