(Problem 2. 20 points) Consider a survey design with three customers (X, Y, Z) who can ask

2 or 3 questions about four products (A, B, C, D), each of which requiring 1 or 2 surveys.

1. Represent the problem as a circulation problem and then as a max-flow problem.

2. Briefly describe how a solution is derived from the max-flow network. You only need to

show one final result for case 1.

3. Suppose Z cannot survey C and D and each product has to be questioned by exactly 2

customers, is a feasible design still possible?

4. If there is more than one solution for case 3, show all integer solutions.