Declaration of variables in large Linear Programming model with NMaximize

Question

I want to solve a large LP problem using NMaximize. This is a small instance of my bigger problem:

$$max \sum^{4}_{t=1}(\sum^{4}_{c=1} V_{c}*f_{c,t})\\ s.t\quad \sum^{5}_{t=1} f_{c,t} \leq 100,\forall t$$

where $ f_{c,t} \geq 0$ and $c=1...5$ and $t=1...5$

I wrote the following:

NMaximize[{Sum[f[c, t]*V, {c, 1, 4}, {t, 1, 4}], 
  Sum[f[c, t], {c, 1, 5}] <= 100}, {f[c, t]}]

How can I declare f[c,t] as a variable?

Answer 1

SeedRandom[42];
n = 3;
Array[(v@# = RandomInteger[100]) &, n]
NMaximize[{
           Sum[f[c, t]*v[c], {c, n}, {t, n}],
           And[And @@ Thread[Flatten@Array[f, {n, n}] >= 0], 
               And @@ Table[Sum[f[c, t], {c, n}] <= 100, {t, n}]]}, 
           Flatten@Array[f, {n, n}]]
(*
{54, 66, 4}

{19800., {f[1, 1] -> 0.,   f[1, 2] -> 0.,   f[1, 3] -> 0., 
          f[2, 1] -> 100., f[2, 2] -> 100., f[2, 3] -> 100., 
          f[3, 1] -> 0.,   f[3, 2] -> 0.,   f[3, 3] -> 0.}}
*)