Class Opener:

• Solve each equation for Y:

1. 3x + y = 3 2. 7 + y = 2x3. x + 2y = 5

4. x – y = -1 5. 4x + 3y = 7 6. 2x – 5y = -3

Linear Programming: Vocabulary

• Linear programming is a technique that identifies the minimum or maximum value of some quantity. This quantity is modeled with an objective function. Limits on the variables in the objective function are constraints, written as linear inequalities.

Feasible Region:

After graphing your constraints you will come up with a feasible region. This shaded portion of your graph will contain all the points that satisfy the constraints.

Using Our Calculators

• Using your calculators sketch a picture of the shape of the feasible region of the following system of inequalities:

Finding the Vertex:

• For each feasible region we come up with we are going to have to find the value (x,y) of its corners.

• The corners are called vertices.

Looking Back:

• Find the value of each vertex of our feasible region that we just graphed.

Using Our Vertices:

• The last thing we must do is plug in the values of our corners to find the maximum and minimum value for a given objective function.

Using our values from our graph plug into the following to find the maximum value and minimum values.

Example:

• Graph the system of constraints. Name the vertices. Then find the values of x and y that maximize and minimize the given objective function:

Student Check:

• Graph the system of constraints. Name the vertices. Then find the values of x and y that maximize and minimize the given objective function:

Practice:

• Linear Programming Basics Worksheet

Exit Slip:

• Graph the system of constraints. Name the vertices. Then find the values of x and y that maximize and minimize the given objective function:

Exit Slip:

• Graph the system of constraints. Name the vertices. Then find the values of x and y that maximize and minimize the given objective function: