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**Department of Mathematics Education**

Flower Shop Dilemma

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 floral
arrangements to sell.

To motivate students, ask about their perceptions of the way
businesses operate. Ask what type of
expenses a florist might incur. Be sure
they understand that in order to make a profit, these expenses must be offset
by the prices affixed to the products sold.
When discussing expenses, students should mention labor cost; therefore,
assume this is a flower shop with the owner as the only employee.

For a Microsoft Word copy, CLICK HERE.

You can have students can work in pairs. Tell them that each pair is to act as a
consulting partnership that has been hired to help the florist achieve her
goals.

For questions 1-5, have students work independently. When students have completed questions 1-5,
partners can compare results and resolve and discrepancies. They can complete 6-8 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, systems of
equations, functions, systems of inequalities, graphing inequalities, and
linear programming. It also has many
entry and exit points.