---

restart:
with(linalg):
X:=array(1..3,1..5):
C:=matrix([[5,4,3,4,0],[3,2,5,5,0],[1,6,3,2,0]]):
F:=sum(sum(C[i,j]*X[i,j],i=1..3),j=1..5):
with(simplex):
minimize(F,{sum(X[1,j],j=1..5)=160,sum(X[2,j],j=1..5)=140,sum(X[3,j],j=1..5)=60,sum(X[i,1],i=1..3)=80,sum(X[i,2],i=1..3)=80,sum(X[i,3],i=1..3)=60,sum(X[i,4],i=1..3)=60,sum(X[i,5],i=1..3)=80,seq(seq(X[i,j]>=0,i=1..3),j=1..5)},NONNEGATIVE);
show(%,F);
XT:=matrix([[0,0,60,80,20],[20,80,0,0,40],[60,0,0,0,0]]);
X:=matrix([[0,0,60,80],[20,80,0,0],[60,0,0,0]]);