Modifies Dijkstra’s Algorithm to find the maximum cost path
This will not work. Consider 


(a)-4->(b) 
(a)-1->(c)
(b)-2->(d)
(c)-6->(d)


Looking for the max cost path from (a) to (d), the max heap will follow (a)-4->(b)-2->(d) and never explore the (a)-1->(c) edge. 

See here for an alternative based on a topological sort.