Minimize Optimization on Two-Dimensional Matrix

Question

z = Array[Subscript[y, ##] &, {3, 2}]
f = {2, 5, 1}
z*f
Total[Flatten[ z*f]]
Minimize[{Total[Flatten[ z*f]], 
  Total[z] == 10 && NonNegative[Min[z]]}, z, Integers]

The above code works for one-dimensional matrix z, But when z is two-dimensional, this error occurs:

Minimize::ivar: {Subscript[y, 1,1],Subscript[y, 1,2]} is not a valid variable. >>

Anyone have any idea why this happens?

Thanks

Answer 1

One has to provide the variables as a flat list. Therefore you just have to replace z with Flatten[z] in your Minimize:

Minimize[{Total[Flatten[z*f]], Total[z] == 10 && NonNegative[Min[z]]}, Flatten@z, Integers]