A company that produces yogurt has plants in four locations: 1) Preston, Idaho 2) New Ulm, Minnesota 3) Carthage, Texas 4) Coalwood, West Virginia. The annual capacity of each plant to produce yogurt is 10,300, 12,400, 11,300, and 12,700 tons, respectively. To cover demand, the company wants to ship 7,700 tons to a distribution center in Modesto, California, 6,200 to South Bend, Indiana, 10,200 to Talladega, Alabama, and 8,400 to Punxsutawney, Pennsylvania. The per ton distribution costs from each plant to cach distribution center are given in the table below: Table: Shipping cost per ton, plant capacity in tons, and distribution center demand in tons Plants Idaho Minnesota Texas West Virginia Requirement S Califor nia $160 $380 $360 $520 7,700 Distribution centers Indiana Alabama $300 $360 $120 $220 $180 $100 $100 6,200 $80 10,200 Pennsylvan ia $380 $200 $240 $60 8,400 Capacity 10,300 12,400 11,300 12,700 In addition to choosing how much yogurt to ship from each plant to each distribution center, the company may also choose which plants to operate. The fixed cost of operating each plant are $500,000 for the Idaho plant, $450,000 for the Minnesota plant, $380,000 for the Texas plant, and $350,000 for the West Virginia plant. Which plants should the company operate, and how many tons of yogurt should be shipped from each plant to each distribution center if the company's goal is to minimize the combined distribution and fixed operating costs? What is the combined cost under the optimal solution? Instructions 1. To solve the problem, proceed as follows: Use the Generalized Optimization Modeling Procedure (GOMP) to set up your problem: i. Define your model in words 1. Identify the firm' s/manager' s objective function in words 2. Identify the decision variables in words 3. Identify the constraints in words ii. Formulate your model mathematically 1. Define the decision variables 2. Define the objective function in terms of decision variables 3. Define the constraints in terms of the decision variables. iii. Set up the problem in Excel and use Solver to find the optimal values of the decision variables. Once you complete the GOMP, use Solver to find the optimal solution and answer the questions asked in the problem. 2. Please submit only one Word or pdf file. Please do not submit your spreadsheet file. The file should include your GOMP that clearly specifies the notation you are using along with answers to any follow-up questions.