Problem 8, Answer the multiple choice questions by providing the single best response.

1.Which of the following statements is why we can stop when we find the optimal solution in the Simplex Method?

1. The minimum ratio rule ensures we are optimal.
2. In standard form all variables must be greater than or equal to zero
3. Canonical form allows us to quickly identify the basic feasible solution.
4. A local optimal solution will be a global optimal solution if the feasible region is convex.

2. To avoid the wind, ACU has decided to create a tunnel system such that students could get from every building to every other building on campus through the tunnel. If ACU is interested in minimizing the amount of digging, what network optimization problem is most appropriate to solve this problem?

1. Assignment Problem
2. Transportation Problem
3. Shortest Path Problem
4. Maximum Flow Problem
5. Minimum Spanning Tree Problem

3. If the feasible region is unbounded, there is no unique optimal solution to a linear programming formulation.

a. True

b. False

4. A network has 6 nodes. How many arcs will there be in the minimum spanning tree solution for this network?

a. 4

b. 5

c. 6

d. 7

e. 8

5. The objective function of the max flow problem is to:

a. maximize the total flow across all arcs in the network

b. maximize the total flow into the sink node(s)

c. maximize the flow into any node in the network

d. maximize the total capacity across all arcs in the network