What is linear programming in Algebra 2 class and what is it used for? This is the foundation of solving linear inequality programming real world problems, which focuses graphing a system of inequalities (constraints) in the first quadrant using the intercepts-method, and then solving the system of inequalities algebraically using either substitution or addition (a.k.a. linear combination) method. Introduces all vocabulary such as feasible region, constraints, boundary points, objective function for a linear programming problem. Then students are given an objective function and they practice plugging in all the boundary points of the feasible region to maximize or minimize something. Students are also exposed to writing their own objective functions and constraints using a graphic organizer.

This introductory linear programming unit goes in perfect scaffolded sequence, where each worksheet builds on the previous skill work and adds more skills to prepare in solving a linear programming real world problem.

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➤ Check out my PART 2 of the series - Linear Programming Problems

➤ Check out my BUNDLE - Linear Programming

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INCLUDED:

✫ Step-by-step answer keys with notes to EVERYTHING!

✫ Full "understanding concepts" lesson - 13 PDF slides

✫ Introductory packet - 4 pages

✫ Four double-sided worksheets (can be used as homework, classwork, Warm Ups, quizzes, etc.). These are scaffolded and written guided-lesson style.

SPECIFICS of Lesson:

➤ The "Understanding Concepts" lesson starts out with asking students: What is a solution? (Answer: Any value(s) that makes an equation, inequality, system of equations, or system of inequalities TRUE.)

➤ Students are given a scenario in which students must write an equation and then graph the line to represent the total number of books you can carry given that algebra books weigh 2 pounds each and geometry books weigh 3 pounds each; and you can carry a total of 36 pounds at one time without straining your back. They visually see the solution set (7 possibilities of combinations).

➤ Then the problem changes a little; where you can carry at most 36 books; now this turns into a linear inequality. Using the visual of the graph in the lesson, students can clearly see there are exactly 127 possible scenarios.

➤ Linear programming connection: Students are asked what is the maximum number of geometry books and algebra books you can carry? This is where vertices of the feasible region is introduced to students.

SPECIFICS of Introductory Packet:

➤ This Getting Ready for Linear Programming packet starts out with defining what linear programming is (a technique that identifies the minimum or maximum value of some quantity). It also introduces what is an objective function, constraints, feasible region, and boundary points.

➤ Students begin by separately graphing the solution to x greater than or equal to zero, then y greater than or equal to zero, and then finally the system of inequalities (both of them on the same graph), which introduces the idea that your solution of a feasible region will always be in the first quadrant. Students are then shown the idea/connection that linear programming problems will be graphed in the first quadrant because we are dealing with real world problems, which realistically involve only non-negative solutions.

➤ Students work on graphing the feasible region for systems of linear inequalities using the Intercepts-Method only in which two of the constraints are also that both x and y are greater than equal to zero. This prepares students for future linear programming problems since they must know how to graph a feasible region and to find the boundary points.

➤ These problems are all scaffolded and written in a guided-lesson way in which students are shown connections between solving the system algebraically and finding the boundary points of the feasible region.

➤ The very last problem exposes and plants the seed to students where an objective function is given to represent the profit for selling cupcakes and cakes, and then where students must practice plugging in the boundary points in order to maximize profit.

SPECIFICS of Guided Lesson Style Worksheets:

➤ Worksheets 1 + 2: Students graph the feasible region of a system of linear inequalities using the intercepts-method, then solve the system algebraically to help them find the last of the 4 boundary points of the feasible region.

➤ Worksheets 3 + 4: Taking worksheets 1 + 2 a step further, students are now given an objective function in which they must plug in the boundary points to maximize/minimize something. Then in other problems, students practice for the first time reading a linear programming problem, where students must come up with their own objective function and system of linear equalities (constraints) using a graphic organizer. Some of these problems will be seen again in my PART 2 Linear Programming series, where students will actually solve the whole problem; not just complete the first 3 steps.