The linear program for widest path or maximum capacity path problem.

Question

I have to give the linear program for the widest path problem or maximum capacity path problem which gives the path where the greatest flow is achieved. I thought of solving it as a Max Min problem. First to find all edges that have the minimum value in each possible path from source to destination and second to find the maximum of these values. I don't know how to implement the first part as a linear program. Can anyone help me? If there is another way to solve the problem I will be grateful to know. Thank you in advance!