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:

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 company's goal is to minimize the combined distribution and fixed operating costs? What is the combined cost under the optimal solution?

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

Plants	Distribution centers	Capacity
California	Indiana	Alabama	Pennsylvania
Idaho	$160	$300	$360	$380	10,300
Minnesota	$380	$120	$220	$200	12,400
Texas	$360	$180	$100	$240	11,300
West Virginia	$520	$100	$80	$60	12,700
Requirements	7,700	6,200	10,200	8,400