A traveler leaving from Beijing and heading to Shenzhen can reduce costs through the various travel options available. The easiest and fastest way would be to take a direct plane, but it will also be the most expensive. He has made these calculations in terms of hours necessary between cities with convenient costs of travel, mixing planes, trains, and buses.

Beijing–Tianjin: 3h Beijing–Lanzhou: 3h Beijing–Shanghai: 15h Lanzhou–Tianjin: 2h 30m Beijing–Hangzhou: 16h Tianjin–Hangzhou: 18h Shanghai–Hangzhou: 1h Shanghai–Xiamen: 10h Lanzhou–Shenzhen: 12h Xiamnen–Shenzhen: 3h Hangzhou–Shenzhen: 6h The distances between the cities have been given in this list but are expressed in terms of hours instead of distance. Design the network model and calculate the shortest path to reach Beijing to Shenzhen in the fastest way.