**Grade 9: Lines and Curves**

Here we use a purely graphical approach to solve three optimization problems. Each problem involves a line and a curve. The students do not have equations for the curves, but simply work with its interaction with the line. The problems develop both local and global approaches.

**Advertising the Concert**

How much advertising should we buy to maximize our profit defined as revenue R from ticket sales minus advertising cost C?

Teacher manual

Student workbook

**Alligator Egg**

We have a large alligator egg just out of the fridge (10 degrees) which needs to be heated to 90. There are two acceptable methods––one is to immerse it in boiling water and the other is to microwave it at LOW power. By coincidence, it turns out that the cooking time is the same for both methods––exactly 10 minutes. Can I lower my cooking time by switching––one method for a certain time and then the other?

Teacher manual

Student workbook

**Lineup**

Folks start arriving to register at 7:00 AM, but the service wicket does not open till 8. At this point folks are served at the constant rate of 5 per minute. Graphs of total arrivals A and departures D are given and the students are asked questions such as what is the maximum length of the lineup and which person stands in line the longest.

When the students are comfortable with these questions, we give them a situation in which the service rate varies, being low for the first 80 minutes and then higher when new staff come on duty.

Teacher manual

Student workbook