For the directed network below
1.Formulate an LP problem to find the shortest path from C to E. The number on an arc is its distance. (Note: The origin is C, not A; the destination is E, not F.)
2.Use Excel Solver to find an optimal solution. Submit the Excel file with
Solver setup and optimal solution saved. (Hint: You do not need to define binary variables in Solver; simply making them non-negative is enough. See Lecture 8 slides Page 22).
3. Write down the mathematical expression for the additional constraint that at most 3 arcs should be on the shortest path.
4. Without re-solving the problem with the additional constraint above, determine whether the optimal solution would change. Why or why not?
5. Write down the mathematical expression for the additional constraint that the shortest path must pass node A.
6. Write down the mathematical expressions for the additional constraint that each node must be visited at least once. (Note: You can imagine that this is a travel plan to visit all the places of interest starting from C and ending at E with the shortest total distance. It is okay to pass a place twice or more if needed.)
3
E
A
2
B
5
3
6
c
D