6 Vocabulary (2.7)Linear Programming: using polygonal convex sets to find maximums or minimums of real world problemsConstraints: conditions of the real life problem. The inequality systems that creates the polygonal convex set.
7 Linear Programming Procedure Define variablesWrite constraintsGraph and find vertices of polygonal convex setWrite an expression whose value is to be maximized or minimizedSubstitute values of the vertices in the expressionSelect the greatest or least value
8 The profit on each set of cassettes that is manufactured by MusicMan, Inc., is $8. The profit on a single cassette is $2. Machines A and B are used to produce both types of cassettes. Each set takes nine minutes on Machine A and three minutes on Machine B. Each single takes one minute on Machine A and one minute on Machine B. If Machine A is run for 54 minutes and Machine B is run for 42 minutes, determine the combination of cassettes that can be manufactured during the time period that most effectively generates profit within the given constraints.
9 Sometimes there might not be a polygonal convex set Infeasible: when the constraints cannot be satisfied simultaneously. (no solution)Unbounded: the region formed by the constraints is not a closed region. (just a minimum or just a maximum value)
10 More than one solution?Alternate Optimal Solutions: when two or more vertices of a polygonal convex set gives the same minimum or maximum