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 each distribution center are given in the table below: Table: Shipping cost per ton, plant capacity in tons, and distribution center demand in tons.

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. Use the GOMP to determine your objective function, decision variables, constraints, and optimal decisions. Which plants should the company operate, and how many tons of yogurt should be shipped from each plant to each distribution center if the companys goal is to minimize the combined distribution and fixed operating costs? What is the combined cost under the optimal solution?

Instructions: 1. To solve each problem, you will need to do the following: a. Use the Generalized Optimization Modeling Procedure (GOMP) to set up your problem as follows: i. Define your model in words 1. Identify the firms/managers 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. b. Answer the questions in each of the problems below. 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.

Tab1e: Shipping cost per ton, plant capacity in tons, and distribution center demand in tons Tab1e: Shipping cost per ton, plant capacity in tons, and distribution center demand in tons