Title III Technology Literacy Challenge Grant

• This learning experience fits into a unit on solving systems of equations and inequalities at the junior or senior level.
• Students will need to know how to graph equations, shade inequalities, work with functions, and how to operate a graphing calculator.

• Apply axiomatic structure to algebra

Mathematics Key Idea #4 (Modeling/Multiple Representation)

• Model real-world problems with systems of equations and inequalities
• Use graphing utilities to create and explore geometric and algebraic models

• Use a computer as a modeling tool
• Identify needs and opportunities for technical solutions from an investigation of situations of general or social interest

• The experience should start out by looking at the possible types of graphs for linear programming. The systems on worksheet #1, taken from the textbook "Advanced Mathematical Concepts" (published by Glencoe), will be graphed on a graphing calculator. Each system will be evaluated and classified as one optimal solution, alternate optimal solutions, infeasible, or unbounded. Students will be required to find the definitions in the textbook. This task will be done individually, followed by a brief group discussion on the results. Students should either sketch the graphs, or if a graph link is possible with a computer, print the graphs. To find the solutions, students will have to use the trace function on their calculators. Then they will have to evaluate the cost functions on paper. All results will be handed to the teacher and graded on an appropriate rubric. After this has been completed, students will form groups of 2 - 4 members and create a system of their own. Creativity is limitless here. If there is access to the Internet, they may do some research on a specific topic before they create the system, which will make the topic seem more real to them, but will also require more time. If time is a problem, they may just make up a system without research. The system must have at least four inequalities and a cost function. When completed, the systems will be given to other groups and be evaluated. The instructor should have some extra systems ready for groups to solve in case some of the created systems are incomplete (which is unlikely because this level of math student can usually handle this task). All groups will be graded on the system created and the system solved.

• The instructor may have to find some Internet sites for the students ahead of time, and might have to decide on just a few products that could be created if the research method is used. Rubrics will be altered, depending on how in depth the experience is allowed to go.

(3 to 5) 40 minute class periods

• graphing calculator
• graphing link from calculator to computer
• worksheet #1
• Internet computers (optional)

• collect printouts from computer and/or calculation papers (work from worksheet #1)
• collect systems after creation
• collect systems after solution
• involvement in the class discussion

• This learning experience is designed to familiarize the students with the graph-making capabilities on the calculator. It also helps students see what companies go through when creating new products. Students will be able to see several sides to the picture; the research, the solution, and the decision on whether the product is feasible to make under certain conditions.

Contracting: The BJ Electrical Company needs to hire master electricians and apprentices for a one week project. Master electricians receive a salary of $750 per week and apprentices receive $350 per week. As part of its contract, the company has agreed to hire at least 30 workers. The local Building Safety Council recommends that each master electrician spend three hours for inspection time during the project. This project should require 25 hours of inspection time. How many of each type of worker should be hired to accomplish the project and still meet the contract safety requirements?

Marketing: Yummy Ice Cream conducted a survey and found that people liked their black walnut flavor three times more than their tutti-frutti flavor. One distributor wants to order at least 20,000 gallons of the tutti-frutti flavor. The company has all of the ingredients to produce both flavors, but it has only 45,000 gallon-size containers available. If each gallon of ice cream sells for $2.95, how many gallons of each type flavor should the company produce?

Manufacturing: The Cruiser Bicycle company makes two styles of bicycles: the Traveler, which sells for $200, and the Tourister, which sells for $600. Each bicycle has the same frames and tires, but the assembly and painting time required for the Traveler is only one hour, while it takes three hours for the Tourister. There are 300 frames and 360 hours of labor available for production. How many of each model should be produced to maximize revenue?

Manufacturing: The Swing-Well Company produces two types of golf clubs: the Driver, which sells for $30, and the Master, which sells for $40. Swing-Well has more orders for the upcoming month than it is capable of producing. Using the production schedule below, what is the maximum revenue that Swing-Well should anticipate for the upcoming month?