operation research

Consider the network given below. The arc lengths and the time it takes to traverse them are given above the arcs in (distance, time) format. Suppose you want to travel from node 1 to node 8 using the shortest path. However, you must also obey the following conditions: i) Node 4 must be visited on the selected path. ii) The total travel time must be less than or equal to 15. ill) The number of visited nodes have to be add on the selected path. Formulate an integer program to decide on the shortest path with the given side constraints. (1,1) (2.4) (2,21 (2,1) 2,3) (6,4) (1,2) (5,4) 8 (1,1) (3,3) (2.12 (7.8) (6,5) (5,4) (8.10) 4 6