There are a variety of free tools available, for example this Graph Creator from the Illuminations site includes the facility to explore Hamiltonian cycles.
For the Simplex method this tool is very easy to use. Selecting Example then Solve shows how to use the applet.
This applet allows you to enter a network and then find the shortest path using Dijkstra’s Algorithm.
Firstly click to draw the nodes, once all the nodes are in place use the drop down menu on the left to draw the arcs.
The documentation at the top desctribes each function.
On a lighter note – some Decision Maths Dancing!