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This lecture covers the preparation for linear programming in the context of linear algebra concepts like linearly independent and maximal independent subsets, rank of matrices. The scenario involves a post office adjusting its full-time employee schedules. Learn how to formulate an LP model to minimize hired staff, understand vertices, feasible domains, slack forms, fundamental theorem, and simplex method employed in LP problem-solving. Dive into proofs, characterizations, optimality conditions, and a detailed exploration of the simplex table method, lexicographical ordering, and pivoting techniques.
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LP examples • A post office requires different numbers of full-time employees on different days of the week. The number of full-time employees required on each day is given in the table. Union rules state that each full-time employee must work five consecutive days and then receive two days off. The post office wants to meet its daily requirements using only full-time employees. Formulate an LP that the post office can use to minimize the number of full-time employees that must be hired.
Optimal occurs at a vertex!!! Feasible domain
