1. Carry on Luggage Problem Several popular models of carry-on luggage have a length 10 in. greater than their depth. To comply with airline regulations, the sum of the length, width, and depth, may not exceed 45 inches. Make a sketch, label, and write down anything that seems important in the top left square.

2. As a passenger, what do you want to know? What color is the luggage? How much did it cost? What size will fit the most stuff? Will my hair dryer fit in? What is the longest golf club I can put in?

3. 1.Find 5 different dimension options that meet the dimension requirements and compute the volume for each. Organize the data in a table and show how all requirements are met. 2.Generate a function equation for Volume in one variable that will also capture the information from your table. Express it in factored form and in standard form. What does your input variable stand for? 3.Predict what you think the graph of the Volume function will look like and make a sketch. Justify your thinking. Be ready to explain how you know your sketch is reasonable in terms of your table, realistic domain, intercepts, range, other behavior.

4. 4.With the tools that you have, find solutions to the questions we generated or write down what you still need to know. Support your thinking. Extension: Some airlines have a carry on luggage tester bin. It has width 9” and length 22”, but the height is open. With these additional conditions what are the dimensions for baggage with the largest volume?

5. Exit Task On back of your paper please respond to: 1.We found a maximum value to solve the problem, but the volume function appears to take on even higher values. What’s an example of an x value that gives one of these higher y values? 2.Why aren’t we considering these higher y values?