Learning Objectives:

__Math Tutoring on Linear Programming__

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**Linear Optimization** or **Linear Programming** is a method used to maximize or minimize a quantity given by a linear equation under certain constraints or restrictions.

A **Linear Programming Problem** consists of:

1) A **linear function** called an **Objective Function** that is to be maximized or minimized.

2) A system of **linear inequalities** called the **constraints. **The solution to the system of inequalities is called** ****Feasible Region. **Steps to Solve a **linear programming problem:**

1) Define the **variables**.

2) Write the objective function and state whether to **maximize** or **minimize** the **function**.

3) Write the **constraints**.

4) Graph the **constraints** and determine the **feasible region**.

5) Identify the vertices of the **feasible region**.

6) Test the vertices in the objective function to determine the **maximum **or** minimum function value**.

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**Hook Questions:**

*1. What is Linear Programming?*

*2. How to use Linear Programming in Maximizing profit?*

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