##
* *Reflection:
Letters & Postcards, Day 2 of 2 - Section 2: What is Linear Programming?

I decided in class that the students needed a bit more practice, so we carefully walked through yet another example of linear programming, paying special attention to the process of interpreting the graphical solution. The biggest challenge seems to be using a movable line to identify the optimum solution. (see the whiteboard) Most students are satisfied instead to determine intuitively the neighborhood of the optimum solution and then to test all the points in that neighborhood. Once I get over my frustration at their rejection of the method I'm teaching, I can accept this. Honestly, it’s a good way to solve the problem, it shows that they clearly understand the meaning of the solution set, and it doesn’t take them much longer than the alternative. In fact, many students can pin down the optimum solution this way in less time than it would take them to write the linear equation.

I’ve decided to focus my attention, then, on interpretation of the graphical solution, rather than on mastery of the technique of linear programming. If students can model the situation and then use that model to find the optimum solution, what more could I want? That's the definition of success in this case!

# Letters & Postcards, Day 2 of 2

Lesson 5 of 15

## Objective: 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.

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

*45 minutes*

#### Choose Your Own Adventure

*15 min*

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!]

*expand content*

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- UNIT 1: Modeling with Algebra
- UNIT 2: The Complex Number System
- UNIT 3: Cubic Functions
- UNIT 4: Higher-Degree Polynomials
- UNIT 5: Quarter 1 Review & Exam
- UNIT 6: Exponents & Logarithms
- UNIT 7: Rational Functions
- UNIT 8: Radical Functions - It's a sideways Parabola!
- UNIT 9: Trigonometric Functions
- UNIT 10: End of the Year

- LESSON 1: What is Algebra?
- LESSON 2: The Music Shop Model, Day 1 of 2
- LESSON 3: The Music Shop Model, Day 2 of 2
- LESSON 4: Letters & Postcards, Day 1 of 2
- LESSON 5: Letters & Postcards, Day 2 of 2
- LESSON 6: Choose Your Own Adventure
- LESSON 7: What Goes Up, Day 1 of 3
- LESSON 8: What Goes Up, Day 2 of 3
- LESSON 9: What Goes Up, Day 3 of 3
- LESSON 10: The Constant Area Model, Day 1 of 3
- LESSON 11: The Constant Area Model, Day 2 of 3
- LESSON 12: The Constant Area Model, Day 3 of 3
- LESSON 13: Practice & Review, Day 1 of 2
- LESSON 14: Practice & Review, Day 2 of 2
- LESSON 15: Unit Test