1 / 9

Linear Programming

Linear Programming . Maximizing and Minimizing Functions using a System of Inequalities. Real World Applications. Many real-world problems consist of maximizing or minimizing a certain quantity subject to some constraints. Most companies are out to maximize their profit!. Here’s the problem:.

evan-hopkins
Download Presentation

Linear Programming

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. Linear Programming Maximizing and Minimizing Functions using a System of Inequalities

  2. Real World Applications • Many real-world problems consist of maximizing or minimizing a certain quantity subject to some constraints. • Most companies are out to maximize their profit!

  3. Here’s the problem: • A nutrition center sells health food to mountain climbing teams. The Trailblazer mix package contains 1 pound of corn cereal mixed with 4 pounds of wheat cereal and sells for $9.75. The Frontier mix package contains 2 pounds of corn cereal mixed with 3 pounds of wheat cereal and sells for $9.50. The center has 60 pounds of corn cereal and 120 pounds of wheat cereal available. How many packages of each mix should the center sell to maximize its profit?

  4. What are we trying to maximize??

  5. We are trying to maximize the profit of the store, which is $9.75 per unit of Trailblazer and $9.50 per unit of Frontier. Let t = # of trailblazer mix sold Let f = # of frontier mix sold C = 9.75t + 9.50f What is the OBJECTIVE FUNCTION?

  6. What are the Constraints? 1) We can't make less than zero of either product. 2) And we have a fixed amount of corn and wheat that we can use. • So, can you think of the constraints? • **Hint: it is going to be a system of inequalities!!

  7. Maximize 9.5f + 9.75t, subject to the constraints: t ≥ 0 f ≥ 0 t + 2f ≤ 60 4t + 3f ≤ 120

  8. To solve a Linear Program: • Identify the variables and write the OBJECTIVE FUNCTION. • For us, it was the formula for the profit which we wanted to maximize. • Figure out the inequalities that represent constraints of the problem. • Graph it. • If it is bounded, the min and max are corner points. • If it is unbounded, it may not attain a maximum or minimum value. • Lastly compute the objective function at all of the points in order to determine the min or max.

More Related