This is a typical transportation problem. If I use matlab to do linear programming, it won't take me long, but the model is easy to build.

Suppose xij is the supply from I factory to J production area.

Ai is the output of I plant bj, and the demand cij freight rate of J area.

Minimum value = sum (cx)

The constraint condition is that the sum of each i xij is ai.

Every JXiji is bj.

It's as simple as that