1 / 5

Lesson 3-4

Lesson 3-4. Linear Programming. The inequalities are called the constraints . The intersection of the graphs is called the feasible region . The intersection of the lines are vertices . When the graph of a system of constraints is a polygonal region like the one

iona
Télécharger la présentation

Lesson 3-4

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lesson 3-4 Linear Programming

  2. The inequalities are called the constraints. The intersection of the graphs is called the feasible region. The intersection of the lines are vertices. When the graph of a system of constraints is a polygonal region like the one graphed at the right, we say that the region is bounded. The maximum or minimum value of a related function always occurs at one of the vertices. The process of finding maximum or minimum values of a function for a region defined by inequalities is called linear programming.

  3. Bounded Region • Graph the following system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the function f(x, y) = 3x + y. x ≥ 1 y ≥ 0 2x + y ≤ 6 (x, y) 3x + y f(x, y)

  4. Unbounded Region • Graph the following system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the function f(x, y) = 5x + 4y. 2x + y ≥ 3 3y – x ≤ 9 2x + y ≤ 10 (x, y) 5x + 4y f(x, y)

  5. Example: A landscaping company has crews who mow lawns and prune shrubbery. The company schedules 1 hour for mowing jobs and 3 hours for pruning jobs. Each crew’s schedule is set up for a maximum of 9 hours per day. Each crew is scheduled for no more than 2 pruning jobs per day. On the average, the charge for mowing a lawn is $40 and the charge for pruning shrubbery is $120. Find a combination of mowing lawns and pruning shrubs that will maximize the income the company receives per day for one of its crews. p ≤ 2 p ≥ 0 m ≥ 0 1m + 3p ≤ 9

More Related