There are two types of linear programming problems discussed, those with 2 decisions variables and those with more than 2 decision variables. The 2 decision variable problems can be solved using the Graphical Solution Method, while the more complex problems require the Simplex Solution Method. Some examples of linear programming being applied in the real world are as follows:
1. Scheduling school buses to minimize the total distance traveled when carrying students.
2. Allocating police patrol units to high crime areas to minimize response time to 911 calls.
3. Scheduling tellers at a bank to ensure customer needs are being met every hour while minimizing the total cost of labor.
4. Picking blends of raw materials in feed mills to produce finished feed combinations at minimum cost.
5. Determining the distribution system that will minimize total shipping costs from several warehouses to various market places
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