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**Department of Mathematics Education**

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.

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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.