1. a) Formulate the MIP model and solve it using CPLEX.

2. b) Formulate the weak formulation of the problem (WUFL) using fractional xij variables and

   solve its LP relaxation.

3. c) Repeat (b) for the strong formulation of the problem (SUFL).

4. d) Suppose now that the facilities have the following capacities: {8000, 14000, 7000, 5500,

   11000}. Modify your formulation in (a) and resolve the problem using CPLEX. Does the

   optimal solution change?

5. e) Reformulate the problem in (d) such that each customer receives goods from one

   warehouse only (single-source problem) and solve it using CPLEX. Does the optimal solution change?

Consider the following UFL problem with 5 facilities and 6 customers: TO: Customer (Cij) Fixed Cost 1 3 5 9 13 4 11 14 10 FROM: Facility 1 Facility 2 Facility 3 Facility 4 Facility 5 Demand (d;) 5 12 8 2 7 15 8 11 9 5000 8 11 10 9 7 14 2000 15 6 11 9 13 15 8 4000 V) 18000 28000 15000 17000 23000 8 13 10 13 16 3000 4000 3000 Consider the following UFL problem with 5 facilities and 6 customers: TO: Customer (Cij) Fixed Cost 1 3 5 9 13 4 11 14 10 FROM: Facility 1 Facility 2 Facility 3 Facility 4 Facility 5 Demand (d;) 5 12 8 2 7 15 8 11 9 5000 8 11 10 9 7 14 2000 15 6 11 9 13 15 8 4000 V) 18000 28000 15000 17000 23000 8 13 10 13 16 3000 4000 3000