XYZ Industries, a leading manufacturer of car components, is considering locating several new assembly plants in the Southwest. These new plants must have a combined production capacity of at least 450,000 units per year and have a combined operating cost that does not exceed $7.5 million per year. The selection team has narrowed the list to four sites in four cities. The management has established a construction cost limit of $45 million for the project. This money will be used to build the combination of plants that provides the maximum yearly profit. Any one of three different-sized plants can be built on the site in City 1, but only one size plant can be built on each of the other sites. All estimates of production capacity, yearly operating cost, yearly profit and construction cost are as follows: Plant Site Production Capacity Operating Cost Yearly Profit Location (S/year) (S/year) City 1 Size 1 Size 2 Size 3 City 2 City 3 City 4 (units/year) 250,000 225,000 200,000 200,000 200,000 225,000 4,000,000 3,500,000 3,000,000 3,000,000 2,500,000 3,000,000 400,000 350,000 300,000 325,000 325,000 275,000 Construction Cost (S) 25,000,000 22,000,000 19,000,000 22,000,000 20,000,000 23,000,000 (a) (15 points) Develop an integer programming formulation to maximize the total yearly profit. Define your decision variables clearly. (b) (10 points) Solve the model you developed in part (a) using OpenSolver and report the optimal solution. Upload the excel file as well when uploading your solutions. (Hint: Optimal objective function value is $725,000)