3 -4 Linear Programming p 139 Algebra 2

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3 -4 Linear Programming (p. 139) Algebra 2 Prentice Hall, 2007

Objectives You will… Model a real-world situation using the LINEAR PROGRAMMING technique. Create a FEASIBLE REGION on a coordinate plane given 3 or more CONSTRAINTS. Recognize and find the MAXIMUM and MINIMUM values of a feasible region.

Definition Linear Programming is a technique used to determine the maximum or minimum value of some quantity based on an objective function.

Process 1. Write inequalities given a list of constraints or restrictions. 2. Graph the inequalities on the same coordinate plane. 3. Locate the coordinates of the vertices of the feasible region. 4. Substitute the values of each vertex point into the objective function to see which produces the highest (max) or lowest (min) value.

Example Suppose you want to buy some tapes and CDs. You can afford as many as 10 tapes or 7 CDs. You want at least 4 CDs and at least 10 hours of recorded music. Each tape holds about 45 minutes of music, and each CD holds about an hour. The “object” is to spend the least amount possible and still get what you want. If tapes cost $8 and CDs cost $12, the objective function is

Example (contin. ) Step 1: Write inequalities based on the constraints. (Define your variables 1 st!) • Can afford 10 tapes… or 7 CD’s… • Want at least 4 CD’s… • Want 10 hours of music, knowing that tapes holds 45 min & CD’s hold 1 hour…

Example (contin. ) Step 2: Graph your inequalities.

Example (contin. ) Step 3: Determine the coordinates of the feasible region.

Example (contin. ) Step 4: Which vertices meet the objective function? What IS the objective function? – Well, if the object is to spend the least amount of money and tapes cost $8 while CD’s cost $12, you want to “minimize” the function – So, test all the vertex points to see which one results in the lowest C value.

Assignment 3 -4 p. 142: 2, 6, 7, 16, 18, 20 Check out the Video Tutor for this lesson at www. phschool. com – Use the Web Code: ate-0304

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