The National Cereal Company produces a Light-Snak cereal package with a selection of small pouches of four different cereals-Crunchies, Toasties, Snakmix, and Granolies. Each cereal is produced at a single production facility and then shipped to three packaging facilities where the four different cereal pouches are combined into a single box. The boxes are then sent to one of three distribution centers where they are combined to fill customer orders and shipped. The diagram at the top of the next page shows the weekly flow of the product through the production, packaging, and distribution facilities (referred to as a supply chain). Ingredients capacities (per 1000 pouches) per week are shown along branches 1-2, 1-3, 1-4, and 1-5. For example, ingredients for 60,000 pouches are available at the production facility as shown on branch 1-2. The weekly production capacity at each plant (in 1000s of pouches) is shown at nodes 2, 3, 4, and 5. The packaging facilities at nodes 6, 7, and 8 and the distribution centers at nodes 9, 10, and 11 have capacities for boxes (1000s) as shown. The various production, packaging and distribution costs per unit at each facility are shown in the following table.

Weekly demand for the Light-Snak product is 37,000 boxes. Formulate and solve a linear programming model that indicates how much product is produced at each facility that will meet weekly demand at the minimum cost.

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Facility 2 3 4 5 6 7 8 9 10 11 Unit cost $0.17 0.20 0.18 0.16 0.26 0.29 0.27 0.12 0.11 0.14 Ingredients Production Packaging Distribution 2 50 9 0 14 12 3 6050 40 0 10 16 12 60 14 4 46 8 19 6 12 50