Please post full and detailed solutions. This is a past paper question for which no mark scheme has been given. Thanks in advance :)

IB2070_A [Question 2] ABC Company is considering four potential car stores for reaching five target regions. The following table provides the fixed preparation costs at each of the car stores and profit made by servicing one unit of product from each car store to each target region. The last row shows the demand in each region and partial supply is possible. In other words, the company does not need to satisfy all of the demand in a region. The capacities of the car stores 1, 2, 3 and 4 are 1000, 700, 1000 and 1200, respectively. Car Store 1 Region 5 80 Preparation Cost 4000 3000 4000 6000 Region 1 100 120 0 60 500 2 3 Unit delivery profit Region 2 Region 3 Region 4 80 20 30 40 60 50 90 60 20 15 0 80 400 700 300 0 4 50 100 250 Demand ABC Company would like to open at most three stores. In addition, demand of a region can be served by only one car store. (a) ABC Company wishes to maximize its profit in determining which stores to open and how to serve the regions from each operated car store. Formulate the problem as an integer programming model. Explain the decision variables and the constraints. (20 marks) (b) Reformulate the problem with the following additional condition. If both regions 1 and 2 are serviced by store 1, then the unit transportation profit from store 1 to regions 1 and 2 increases from 100 and 80 to 110 and 90, respectively. (13 marks)