Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

3.4 Pp

537 views

Published on

Published in: Technology, Business
  • Be the first to comment

  • Be the first to like this

3.4 Pp

  1. 1. <ul><li>Bell Ringer: </li></ul><ul><li>Graph the system of inequalities from problem # 36 on your homework last night. </li></ul><ul><li>2. Is (-1,1) a solution of the system? </li></ul><ul><li>Why or why not? </li></ul>
  2. 2. Solve linear programming problems. Objective
  3. 3. optimization linear programming constraint feasible region New Vocabulary
  4. 4. Check It Out! Example 1 Graph the feasible region for the following constraints. (Hint: Find the vertices) x ≥ 0 y ≥ 1.5 2.5 x + 5 y ≤ 20 3 x + 2 y ≤ 12
  5. 5. Yum’s Bakery bakes two breads, A and B . One batch of A uses 5 pounds of oats and 3 pounds of flour. One batch of B uses 2 pounds of oats and 3 pounds of flour. The company has 180 pounds of oats and 135 pounds of flour available. Write the constraints for the problem and graph the feasible region. Example 1: Graphing a Feasible Region
  6. 6. Graph the feasible region.
  7. 7. The feasible region is a quadrilateral with vertices at (0, 0), (36, 0), (30, 15), and (0, 45). Check A point in the feasible region, such as (10, 10), satisfies all of the constraints. 
  8. 8. Why would we want to find a feasible region? objective function:
  9. 11. Yum’s Bakery wants to maximize its profits from bread sales. One batch of A yields a profit of $40. One batch of B yields a profit of $30. Use the profit information and the data from Example 1 to find how many batches of each bread the bakery should bake. Example 2: Solving Linear Programming Problems
  10. 12. Example 2 Continued Step 1 Let P = the profit from the bread. Write the objective function: P = 40 x + 30 y Step 2 Recall the constraints and the graph from Example 1. x ≥ 0 y ≥ 0 5 x + 2 y ≤ 180 3 x + 3 y ≤ 135
  11. 13. Example 2 Continued Step 3 Evaluate the objective function at the vertices of the feasible region. Yum’s Bakery should make 30 batches of bread A and 15 batches of bread B to maximize the amount of profit. ( x , y ) 40 x + 30 y P($) (0, 0) 40(0) + 30(0) (0, 45) (30, 15) (36, 0)
  12. 14. Ticket out the Door Use your own words to define Vertex Principle of Linear Programming.

×