2 Linear ProgrammingMethod for finding a minimum or maximum value given constraints(limits).The constraints come from a system of linear inequalities.The graph of the system is call the feasible region.
3 Objective FunctionModels the quantity you are trying to maximize or minimize.Often cost or profitEx: the objective function is C = 2x + yGraphs of lines with various values for C are parallelIf there is a max or min for the objective function, it occurs at one or more of the vertices of the feasible region.This is called the Vertex Principleof Linear Programming
4 Testing VerticesWhat point in the feasible region maximizes P for the objective function P = 2x + y?Graph the system to find the feasible region.Vertices:(0,2.5)(3,1)(2,0)(0,0)Evaluate P at each vertex.P has a maximum value of 7 at (3,1).
5 Using Linear Programming You have at most 20 hours to make T-shirts &sweatshirts.You want to spend no more than $600 on supplies.You want to have at least 50 items to sell.
6 Continued How many of each to maximize profit? Create the constraints: So the objective function is: P = 6x + 20yGraph constraints:Test vertices:(50,0)(25,25)(75,15)(120,0)P is maximized at (75,15)Sell 75 t-shirts and 15 sweatshirts.