set x inputs /bread, meat, milk/
    z outputs /meal1, meal2, meal3/;

alias (x,xx);
alias (z,zz);

table aa(x,xx) quadratic price coefficients
        bread    meat    milk
bread   -0.01   0.003   0.002
meat    0.003   -0.05   0.001
milk    0.002   0.001   -0.07

table bb(z,zz) quadratic quantity coefficients
         meal1   meal2   meal3
meal1    0.050   0.000  -0.003
meal2    0.000   0.060  -0.002
meal3   -0.003  -0.002   0.075

table gg(x,z) effect of quantity on price
         meal1   meal2   meal3
bread    0.003   0.000   0.000
meat     0.000   0.004   0.000
milk     0.000   0.000   0.005

parameter a(x) price constants
        /bread 100,
         meat   50,
         milk   75/;

parameter b(z) quantity coefficients
        /meal1 0,
         meal2 0,
         meal3 0/;

parameter ps(x) prices
        /bread 1.00,
         meat  4.00,
         milk  1.89/;

variables p(x)  input prices
          q(z)  output levels
          u     utility;

positive variable q(z);

equations cost  household cost function
          utility utility function;

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)))+
          sum((x,z),p(x)*q(z)*gg(x,z)) =l= 450.0;
utility.. q("meal1")**.3*q("meal2")**.4*q("meal3")**.3 =e= u;

q.lo(z) = 0.001;
p.fx(x) = ps(x);

model port using /all/;
solve port using nlp maximizing u;