How do you model a problem in which you have two or more variables that must total less than a specific amount? For example, how can you find how many of each type of stamp you need on a package that requires an exact amount of postage? In this lesson you will learn how to represent solutions and constraints to linear inequalities by graphing. Let’s Review You can graph an inequality in two variables. 5x + 6y ≤ 30 A Common Mistake Not accounting for a constraint Can’t I just keep adding stamps until I have enough money? If you only have certain kinds of stamps, you might pay too much! Core Lesson You need $1.00 worth of postage to mail a package. Entire book of $0.03 stamps but only four $0.32 stamps How many of each type can you use? Core Lesson (amount of money using $0.03 stamps) (amount of money + ≥ $1.00 using $0.32 stamps) $0.03(x) + $0.32(y) ≥ $1.00 Core Lesson $0.03(x) + $0.32(y) ≥ $1.00 Constraints: 1. Positive numbers only 2. Whole numbers You will need at least 12 $0.03 stamps and 2 $0.32 stamps. In this lesson you have learned how to represent solutions and constraints to linear inequalities by graphing. Guided Practice Your school needs at least 35 students to help volunteer at a shelter downtown. Seven students can ride to the shelter in each van, and five students can ride in each car. Draw a graph showing all of the combinations of vans and cars possible for the problem. Guided Practice Extension Activities Choose two types of fruit, such as strawberries and watermelon. Write an equation for and graph a linear inequality to show how much of each fruit you could buy without spending more than $10 total. Extension Activities Draw a polygon on a coordinate plane. Write a series of linear inequalities that, graphed and shaded correctly, would result in the given polygon. Quick Quiz An air cargo plane can transport as many as 15 regular shipping containers. One supersized container takes up the space of 3 regular containers. Write and graph a linear inequality to show this situation, and find two solutions to this problem. Quick Quiz Your school needs at least 35 students to help volunteer at a shelter downtown. Seven students can ride to the shelter in each van, and five students can ride in each car. Find the minimum number of cars needed if three vans are available.