Department of Mathematics Education

# EMAT 6700, J. Wilson

Trail Mix

J. Matt Tumlin

The problem of how to minimize cost and maximize profit can be solved with a system linear of inequalities.  Students will be asked to explain the meaning of various systems of equations and inequalities.  Then they will graph the systems and use the graphs to find the optimal way to manufacture trail mix.

To motivate students, ask if anyone has gone backpacking.  Explain about the limits for the weight of a backpack.  Discuss the importance of considering the amounts of certain nutrients in the foods that are packed.

## Directions

You can have students can work in pairs.  For question 2, each pair can solve the first system by substitution while the other solves by graphing.  They can reverse roles for question 5.  They can complete 1,3, and 4 together.

When completed, bring the class together and compare and discuss the results.  Encourage students to share any insights they have gained on linear programming.

This problem has many aspects you can go into, functions, systems of equations, systems of inequalities, graphing inequalities, and linear programming.  It also has many entry and exit points.