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## Objective

SWBAT use systems of linear inequalities to find maximum and minimum solutions.

#### Big Idea

What's the best price to set for that cup of fresh lemonade? Take your lemonade stand to the next level with systems of equations and inequalities.

10 minutes

## Put it Into Action

40 minutes

You will need copies of the Linear Programming problems handout for this section of the class.  Now that we've worked through an entire linear programming problem as a class, I tell my students that they get to work with their back-partner to solve some problems on their own. I remind them to write the constraints, then graph them, and finally use the points of intersection on the graph to find the desired solution.  I distribute the Linear Programming problems handout and ask if there are any questions. (MP1, MP2, MP4) While my students are working I walk around offering encouragement and redirection as needed.  When everyone is done, I ask them to take a "gallery walk" to check their work against the answers I've posted around the room and ask questions about any they don't understand.

## Wrap it Up

5 minutes

I really want my students to remember how important it is to start with good, meaningful equations so I give them a different kind of challenge to wrap up this lesson.  I present them with a Linear Programming Challenge all set up with equations, a graph and a solution - except it's the wrong solution.  My challenge to my students is that they figure out why it's wrong, where the mistaken assumption is.  (MP1, MP2, MP6)  This also sets up the lesson for tomorrow, which focuses on whether the solutions are actually viable answers to the problem.