SWBAT write a system of linear inequalities and use the system to answer questions about balancing time and cost in a real world context. SWBAT explain their solutions to a modeling problem to their peers and respond to the explanations given by others.

Systems are useful mathematical models for situations with a several of constraints. Time is money!

20 minutes

15 minutes

For the final 15 minutes of class, students will be assigned new groups of about 3 students each and given the following assignment:

*Write a real-world problem that may be solved with linear programming. Be creative, but keep it realistic, too! Your problem must have at least three constraints on two variables and require us to optimize a third variable in some way.*

*We'll begin today, but this will be finished as an in-class assignment tomorrow. Have fun!*

Please see the next lesson: **Choose Your Own Adventure**!

Be prepared to help students narrow the number of variables down to two, and a third that can be expressed as a function of the other two. Also, encourage them to be fun and creative, and remind them that the solution set doesn't have to be restricted to the first quadrant. It's interesting to see what sorts of variables students come up with that may be either positive or negative!

[For the record, the Music Shop Problem was originally written by a student named Jake Garcia!]