1. (Uninformed search) (a) [15 points] Construct a graph search problem with no more than 10 nodes for which of the following are true: i. Least-cost search returns an optimal solution. ii. Breadth-first search returns the highest-cost solution iii. Depth-first search returns a solution whose cost is strictly less than the highest-cost solution and strictly more than the least-cost solution. Note that this means your search problem must have at least 3 goal nodes of differing costs. Be sure to include and formally describe each component the graph search problem. 1. (Uninformed search) (a) [15 points] Construct a graph search problem with no more than 10 nodes for which of the following are true: i. Least-cost search returns an optimal solution. ii. Breadth-first search returns the highest-cost solution iii. Depth-first search returns a solution whose cost is strictly less than the highest-cost solution and strictly more than the least-cost solution. Note that this means your search problem must have at least 3 goal nodes of differing costs. Be sure to include and formally describe each component the graph search