Question $1\mathrm{.}1-$ True$/$False

The k$-$center facility location problem can be solved in polynomial time for any given value of k$.$

Question $1\mathrm{.}2-$ True$/$False

Main factor that makes the facility location problem computationally expensive $($or NP$.$hard$)$ is the assignment of

customers to opened facilities, which cannot be solved in polynomial time.

Question $1\mathrm{.}3-$ True$/$False

The traveling salesman problem may be solved by an enumerative algorithm in polynomial time.

Question $1\mathrm{.}4-$ True$/$False

While the Dijkstra's algorithm can solve the shortest path problem in polynomial time, mathematical optimization model

cannot be solved in polynomial time because it is Integer Programing $($IP$).$