The entire graph represents the whole area that we need to search. It is divided into 18 small areas which represents the regions that we need to cover in the optimal flight problem. We will model it as a set covering problem. The objective is to find the minimum number of points where the plane should be in order to cover the whole area

We are assuming that the camera on the plane is rotating at 360^o. It will cover the areas below it and all the surrounding area. For example, if the plane is above1, it will cover areas 1, 2, 4, and 5

The optimal value is Z = 2

The optimal solution is X₅ = 1, X₁₄ = 1, X_i = 0 where i = 1,2,3,4,6,7,8,9,10,11,12,13,15,16,17,18

This implies that if the plane is above area 5 and area 14, it will cover the whole searched area.

This problem will model the following graph as a transportation problem. The graph is divided into 6 smaller rectangles which represent the areas that we need to search for the Optimal Flight Plan problem. The is a cost associated with each path. The objective of this problem is to find the minimum cost flight profile to reconnoitre the area without gaps in the coverage.

We divided the search area into six smaller areas: the plane’s camera is capable of completely covering on the these smaller areas at a time. Therefore we can consider each of these smaller areas as a node and require that the plane visit each of these nodes once.

The plane can travel in a different directions between each node and there are different costs associated with each path. We consider these paths to be arcs. For example, if the plane is above area 1, it can take the route to area 2 (i.e. going east) or to area 4 (i.e. goining south) or to area 5 (i.e. going south-east)

The optimal paths are as follows and the optimal solution is $18.