Gary Gopher wishes to find the quickest way to get to the compost bin from his home in his series of underground tunnels he has developed in a University professor$$s back yard. $($Sometimes there are some very tasty morsels in the compost bin$).$ Dogs and armadillo$$s prowl the area, so speed and staying underground is of the essence.

Nodes in his tunnel network represent the pertinent features in the yard. The link$/$arc values represent $$effort$$ to move from node to node $($say$,$ measured in ergs?$).$ Suggestion: GG may choose to move laterally in his tunnel network $($e$.$g$.,$ between the holly and the redbud$)$ but certainly wouldn$$t move backwards $($e$.$g$.,$ sunburst locust to the small oak$).$ You can model accordingly. The picture shows double arrows where appropriate.

a$)$ Create a LP model to find this least effort path from home to the compost bin for Gary G$.$

b$)$ Augment the model and force Gary G$.$ to travel past two trees on his way to the compost bin.