Formulating a linear programming problem from words into mathematical symbols

I have to solve a network flow problem. I have an idea of what to do but I don't know how to formulate it into mathematical symbols. Here is the problem formulation in words, maybe someone can help me with the mathematical formulation or give me tips on what to do (The assignment question is posted below the formulation if more context is needed) :

Objective function: minimize the maximum of the link loads

i.e min max(linkloads) 

w= max(linkloads) 

therefore the new objective function is min w

Equality constraint: Ax=b  (Node balance)

Inequality constraint: w >= the sum of the blue and red flow in every link regardless of the direction

sign restriction:  x, w >= 0