a) Formulate this problem as an IP to minimize total cost (Define decision variables, objective function and constraints). Hint: There are 3 type of decision variables.

b) Add constraint(s) to ensure the following conditions are satisfied.

- If distribution center 1 is operating, it should serve customer area 2.

- Distribution center 2 and 3 cannot be selected at the same time.

- Stark Industries want to open exactly 2 distribution centers.

(30 Points) Stark Industries produces a type of robot at five different plants. The capacity of each plant is given in table below. SI should supply this robot to 4 type of customer areas. Demand of each customer areas are given in the table below. The company is investigating 3 possible locations for distribution centers, and it requires that each customer areas be served from only one distribution center. Cost of producing a robot at each plant and shipping to each possible distribution center as well as cost of shipping a robot from each distribution center to each customer area are given in the table below in dollars. There is also a fixed operating cost of distribution centers. This cost is same for all distribution centers and it is 100$. Plant 1 2 3 4 5 Capacity 300 200 250 300 400 Customer Area 1 2 3 4 300 Demand 300 200 250 From Distribution Center 1 To Distribution Center 2 5 10 6 11 Plant 1 Plant 2 Plant 3 Plant 4 Plant 5 Distribution Center 3 12 7 5 7 8 6 5 6 7 10 5 Customer Area 4 From Dist. Center 1 Dist. Center 2 Dist. Center 3 Customer Area 1 12 10 Customer Area 2 Customer Area 3 15 6 15 7 23 9 7 20 18 11