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3-4 Linear Programming (p. 139)

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 .

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3-4 Linear Programming (p. 139)

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  1. 3-4 Linear Programming(p. 139) Algebra 2 Prentice Hall, 2007

  2. 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.

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

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

  5. 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 least10 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

  6. Example (contin.) Step 1: Write inequalities based on the constraints. (Define your variables 1st!) • 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…

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

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

  9. 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.

  10. 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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