Department of Mathematics Education

# EMAT 6700, J. Wilson

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.

## Directions

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.