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Metro Food Services Company delivers fresh sandwiches each morning to vending machines throughout the city. The company makes three kinds of sandwiches – ham and cheese, bologna and chicken salad. A ham and cheese sandwich requires a worker 0.45 minutes to assemble, a bologna sandwich requires 0.41 minutes, and a chicken salad sandwich requires 0.50 minutes to assemble. The company has 960 available minutes each night for sandwich assembly. Vending machine capacity is available for 2000 sandwiches each day. The profit for a ham and cheese sandwich is $0.35, for a bologna sandwich is $0.42, and for a chicken salad sandwich is $0.37. The company knows from past sales records that its customers buy as many or more of the ham and cheese sandwiches than the other two types combined. Lastly, customers need a variety of sandwiches available, so Metro stocks at least 200 of each.
Write the linear programming formulation to determine how many of each sandwich it should stock to maximize profit.
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