3.4 Linear Programming 9.2.4.5 Solve linear programming problems in two variables using graphical methods.

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Presentation transcript:

3.4 Linear Programming Solve linear programming problems in two variables using graphical methods.

Guiding Question: How can we apply linear programming?  Lesson Objective: I will be able to apply linear inequality systems to situations and solve them.

Guiding Question: How can we apply linear programming?

Key Words: Linear Programming, Constraint, Feasible Region, Objective Fcn.  Linear Programming – A way to find a maximum or minimum for a set of conditions called constraints.  Constraint – Linear Inequality (acts as a boundary)  Feasible Region: The area within all the constraints

Guiding Question: How can we apply linear programming?

 Objective Function – The function you are trying to maximize or minimize.  The Bakery bakes cupcakes and cookies. A batch of cupcakes uses 5 lbs. of sugar and 3 lbs. of flour. A batch of cookies uses 2 lbs of sugar and 3 lbs of flour. The Bakery has 180 lbs of sugar and 135 lbs of flour. Write the constraints and graph a feasible region.

Guiding Question: How can we apply linear programming?  The Bakery wants to maximize profit. The Bakery makes $40 on each batch of cupcakes and $30 on each batch of cookies. How much of each batch should the Bakery make to make the most money?  Objective Function in this case: 40x + 30y

Guiding Question: How can we apply linear programming?  Assignment Pg. Blue Worksheet