## 3.7 Linear Programming

In this lesson I will teach you linear programming. From my experience this is one of the most difficult topics for algebra students so make sure you set aside enough time to learn and practice the material. Basically, linear programming is a powerful method to help us discover the best way to do something. This "best way" to approach a situation is called "optimization" and this is a key term when we study linear programming. A quick example of linear programming would be to find the optimal number of hours a chemical plant should run in a month to maximize profits. Let's think about for a second- if a chemical plant ran 24/7 for a month we might produce way more product than we can sell and in doing so spent a lot of extra money. However, if we don't run the chemical plant enough during the month we might not make enough product for demand. So, you can see that there is a "best" way of running the chemical plant such that it produces the best profits. These type of problems can be solved using linear programming. A word of warning: linear programming problems can take a long time to solve so be prepared and patient. Make sure you have mastered all the other lessons in the system chapter before taking on this lesson. Even though the topic can be a little difficult it's a wonderful illustration of how math helps us solve problems in the real world.

__DIRECTIONS:__

- Watch The
**Lesson Video**First - Take Good Notes. - Next, Scroll All The Way Down The Page To View The
**Practice Problems**- Try Them On Your Own. - Check The Solutions To The Practice Problems By Looking At The Answer Key At The End Of The Worksheet.
- However,
**YOU MUST Still Watch The Video Solutions To The Practice Problems**; These Are The Videos Labeled EX A, EX B, etc. - They Are Located Next To The Lesson Video. - After Doing All Of The Practice Problems - Complete The Section and Advance To The Next Topic.

**Practice Problems:**