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Solve problems by using linear programming.

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Presentation on theme: "Solve problems by using linear programming."— Presentation transcript:

1 Solve problems by using linear programming.

2 Linear Programming Method 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 Function Models the quantity you are trying to maximize or minimize. Often cost or profit Ex: the objective function is C = 2x + y Graphs of lines with various values for C are parallel If 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 Principle of Linear Programming

4 Testing Vertices What 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 + 20y Graph constraints: Test vertices: (50,0) (25,25) (75,15) (120,0) P is maximized at (75,15) Sell 75 t-shirts and 15 sweatshirts.

7 Assignment Odds p.160 #11-23

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