Get out your Vertices Worksheet!

You will be able to find the maximum and minimum values of a function over a region.

You will be able to solve real-world optimization problems using linear programming.

Today’s Objectives:

Warm UpGraph the following system of inequalities. Find the coordinates of the THREE vertices.

Solve the system of equations.2. by Substitution 3. by Elimination

Jackie has a total of 50 nickels and pennies. She has 13 more pennies than nickels. How many of each does she have?

3.3 Linear Programming

New Vocabulary:

1. Linear Programming-

2. Feasible Region-

3. Bounded-

4. Unbounded-

5. Optimize-

3.3 Linear Programming

Linear Programming:

3.3 Linear Programming

Feasible Region:

Bounded vs. UnboundedThe feasible region is enclosed, or bounded, by the constraints. The maximum and minimum always occur at a vertex.

Bounded vs. UnboundedThe feasible region is open, or unbounded, and can go on forever.

Bounded ExampleGraph the following system of inequalities. Name the coordinates and find the vertices of the feasible region. Find the maximum and minimum values of this region.

Unbounded ExampleGraph the following system of inequalities. Name the coordinates and find the vertices of the feasible region. Find the maximum and minimum values of this region.

ExamplesGraph the following system of inequalities. Name the coordinates and find the vertices of the feasible region. Find the maximum and minimum values of this region.

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You Try One!Graph the following system of inequalities. Name the coordinates and find the vertices of the feasible region. Find the maximum and minimum values of this region.

Linear Programming—Optimization

Optimize:

7 Steps of Optimization

Step 1: Define the variable

Step 2: Write a system of inequalities

Step 3: Graph the system of inequalities

Step 4: Find the coordinates of the vertices of the feasible region.

Step 5: Write a linear function to be maximized or minimized.

Step 6: Substitute the coordinates of the vertices into the function.

Step 7: Select the greatest or least result. Answer the problem.

Linear Programming WorksheetEach week, Mackenzie can make 10 to 25 necklaces and 15 to 40 pairs of earrings. If she earns profits of $3 on each pair of earrings and $5 on each necklace, and she plan to sell at least 30 pieces of jewelry, how can she maximize profit?

Ticket Out The Door

Work through Ingrid’s optimization problem on the worksheet!

Turn in your worksheet on the back table.

HOMEWORK

Lesson 3.3Pg. #’s 14, 16, 17, 20, 23, and 24