Question Type 7: Applying the postman problem to real world contexts Exercises

A worker must clear debris along the four edges of a rectangular block with intersection nodes A, B, C, D in that order. The street lengths are AB = 2 km, BC = 3 km, CD = 2 km, and DA = 3 km. Find the minimum distance required to start and end at A while traversing each street at least once.

A postal worker must deliver mail along three streets connecting intersections A, B, and C. The streets have lengths AB = 5 km, BC = 5 km, and AC = 5 km. What is the length of the shortest closed route that covers each street at least once?

Intersections X, Y, Z are connected in a T-shape: X–Y=6 km and Y–Z=4 km. A road worker must start and end at X, covering each street at least once. What is the minimum route length?

A garbage truck must traverse a straight path of streets between intersections A–B (4 km), B–C (3 km), and C–D (5 km), then return to A. Determine the length of the shortest closed route covering each street at least once.

A municipal inspector must check each road of a small network: a central junction B connects to A, C, D, E via roads BA=3 km, BC=5 km, BD=4 km, BE=2 km. Find the length of the shortest closed route covering all roads at least once.

A road network has nodes A–B=2 km, B–C=4 km, C–D=5 km, D–E=6 km, and a branch C–F=3 km. A maintenance vehicle must start and end at A, covering each road at least once. What is the minimum distance?

Consider the network on nodes A, B, C, D with edges AB=3 km, BC=4 km, CD=5 km, DA=6 km, AC=2 km, BD=1 km. Determine the minimum distance for a closed route covering every edge at least once.

In a small town, five roads form a pentagon A–B=4 km, B–C=3 km, C–D=5 km, D–E=2 km, E–A=6 km, plus a chord A–C=4 km and B–D=7 km. Find the length of the shortest closed route covering each road at least once.

A mail carrier travels on one-way streets forming a directed network: A→B=3 km, B→C=4 km, C→A=5 km, B→D=2 km, D→B=2 km. Determine the length of the shortest closed route that covers each one-way street at least once.

A courier must use these one-way streets: A→B=3 km, B→C=4 km, C→A=5 km, B→D=2 km and D→C=1 km. Find the minimum distance of a closed route covering each directed street at least once.

A delivery service operates on a mixed network: two-way streets are A–B (3 km), B–D (1 km), C–D (5 km); one-way streets are B→C (4 km) and D→A (2 km). What is the length of the shortest closed route that traverses every street in its allowed direction at least once?