all one question

PART C: (4 marks] A distribution company wants to minimize the cost of transporting goods from its warehouses A, B, and C to the retail outlets 1, 2, and 3. The costs for transporting one unit from warehouse to retailer is given by the following table. RETAILER WAREHOUSE 1 2 3 A 15 32 21 B 9 7 6 11 18 5 Demand 200 150 175 The fixed cost of operating a warehouse is $500 for A, $750 for B, and $600 for C, and at least two of them have to be open. The warehouses can be assumed to have unlimited capacity. Management would like to develop a linear programming (LP) model to decide which warehouses should be opened and the amount to be shipped from each warehouse to each retailer. Define the decision variables as follows. Let Xij denote the amount shipped from warehouse i to retailer j (for i = A, B, C and j = 1, 2, 3). Let Yi equal 1 if warehouse i is opened and equal 0 if it is not (for i = A, B, C). Note that each warehouse (if it is opened) cannot supply more than the total demand of 525 units. Given these decision variables, answer the following questions: 1) Write the objective function of the LP model. 2) Write the supply constraint corresponding to warehouse A 3) Write the demand constraint corresponding to retailer 2. 4) Write the constraint that stipulates that at least two of the warehouses have to be open