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 different production facility and then shipped to three packaging facilities, where 1

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7 Ingredients Production Packaging Distribution 16 12 19 50 46 60 50 40 12 60 14 50 14 11 55 12 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 following diagram shows the weekly flow of the product through the production, packaging, and distribution facilities (referred to as a “supply chain”):
Ingredients capacities (per 1,000 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 1,000s 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 (1,000s) as shown.
The various production, packaging, and distribution costs per unit at each facility are shown in the following table:
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 Weekly demand for the Light-Snak product is 37,000 boxes.
Formulate and solve a linear programming model that indicates how much product must be produced at each facility to meet weekly demand at the minimum cost. LO.1