solve all parts please

explanation and keep your answer short. III. (20 points) Blue Computers currently has two manufacturing plants - one in Kentucky and the other one in Pennsylvania. The two plants serve the entire country, which is divided into three regional markets; North, Middle, and West. The capacity of each plant, the demand of each regional market, and the variable production \& transportation cost are shown in the table below. Plant Canacitv. Demand and Production \& Transport Cost per Computer for Blue Computers Blue Computers is anticipating a growth in demand oy su\% at cavingionur. is not sufficient to meet the increased demand. The supply chain manager has explored plant construction costs in adding more capacity to the existing plants. (You can consider this as adding a new plant at Kentucky and Pennsylvania). Capacity can be added in either 400 or 600 units to both existing plants, but not both in each site. Adding 400 incurs a one-time cost of 200,000 , and adding 600 incurs a one-time cost of 300,000 regardless of the site location III. 1. What decision variables do you need to define? How many decision variables in total? (5 points) III.2. What is the objective function? (4 points) III.3. Write the supply constraint associated with Kentucky. (4 points) III.4. Write the demand constraint associated with West market. (4 points) III.5. Discuss in general the pros and cons of adding two small plants in both sites vs. adding only one large plant in one site. (3 points) III.6. If the plan is to add capacity to only one site, how can you address the requirement in the formulation' (2 bonus points) Which site is most likely to get the added capacity? Why? (2 bonus points)