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Linear Programming: Formulate Variables, Objectives and Constraints

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Problem: Cauchy Canners produces canned whole tomatoes and tomato sauce. This season, the company has available 3,000,000 kg of tomatoes for these two products. To meet the demands of regular customers, it must produce at least 80,000 kg of sauce and 800,000 kg of whole tomatoes. The cost per kilogram is $4 to produce canned whole tomatoes and $3.25 to produce tomato sauce. Labor agreements require that at least 110,000 person hours be used. Each kilogram can of sauce requires 3 minutes for one worker, and each kilogram can of whole tomatoes requires 6 minutes for one worker. How many kilograms of tomatoes should Cauchy use for each product to minimize cost? (For simplicity, assume production of y1 kg of canned whole tomatoes and y2 kg of tomato sauce requires y1 + y2 kg of tomatoes.)

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