1 / 11

Solving Linear Programming Problems: Strategies and Examples for Profit Maximization

This guide provides essential steps for solving linear programming problems, including understanding the problem, translating it into mathematical terms, and determining the objective equation. It uses real-world examples—like optimizing almond and walnut purchases for a grocer and planning a school trip transportation to minimize costs—to illustrate these techniques. Learn how to identify constraints, apply methods such as Cover-Up and Elimination, and ultimately maximize profits while minimizing expenses through practical exercises.

hasad-perkins
Télécharger la présentation

Solving Linear Programming Problems: Strategies and Examples for Profit Maximization

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. Section 3.4 LINEARPROGRAMMINGDay 2

  2. Steps of Problem Solving • Understand the problem • Translate the problem • Solve • List all of your restraints • Determine your Objective Equation (usually dealing with Profit) • Use Cover-up to determine the intercepts • Use Elimination/Substitution to determine the intersection points • Check

  3. Example 1 A grocer buys cases of almonds and walnuts. Almonds are packaged 20 bags per case. The grocer pays $30 per case of almonds and makes a profit of $17 per case. Walnuts are packaged 24 bags per case. The grocer pays $26 per case of walnuts and makes a profit of $15 per case. He orders no more than 300 bags of almonds and walnuts together at a maximum cost of $400. Use x for cases of almonds and y for cases of walnuts.

  4. Example 1 A grocer buys cases of almonds and walnuts. Almonds are packaged 20 bags per case. The grocer pays $30 per case of almonds and makes a profit of $17 per case. Walnuts are packaged 24 bags per case. The grocer pays $26 per case of walnuts and makes a profit of $15 per case. He orders no more than 300 bags of almonds and walnuts together at a maximum cost of $400. Use x for cases of almonds and y for cases of walnuts. X = Cases of Almonds Y = Cases of Walnuts

  5. Example 1 A grocer buys cases of almonds and walnuts. Almonds are packaged 20 bags per case. The grocer pays $30 per case of almonds and makes a profit of $17 per case. Walnuts are packaged 24 bags per case. The grocer pays $26 per case of walnuts and makes a profit of $15 per case. He orders no more than 300 bags of almonds and walnuts together at a maximum cost of $400. Use x for cases of almonds and y for cases of walnuts. X = Cases of Almonds Y = Cases of Walnuts (0, 12.5)Using Cover Up (9, 5) Using Elimination (0, 0) (13.3, 0) Using Cover Up

  6. Example 1 A grocer buys cases of almonds and walnuts. Almonds are packaged 20 bags per case. The grocer pays $30 per case of almonds and makes a profit of $17 per case. Walnuts are packaged 24 bags per case. The grocer pays $26 per case of walnuts and makes a profit of $15 per case. He orders no more than 300 bags of almonds and walnuts together at a maximum cost of $400. Use x for cases of almonds and y for cases of walnuts. X = Cases of Almonds Y = Cases of Walnuts

  7. Example 1 A grocer buys cases of almonds and walnuts. Almonds are packaged 20 bags per case. The grocer pays $30 per case of almonds and makes a profit of $17 per case. Walnuts are packaged 24 bags per case. The grocer pays $26 per case of walnuts and makes a profit of $15 per case. He orders no more than 300 bags of almonds and walnuts together at a maximum cost of $400. Use x for cases of almonds and y for cases of walnuts. X = Cases of Almonds Y = Cases of Walnuts How many cases of almonds and walnuts maximize the grocer’s profit? 9 cases of almonds and 5 cases of walnuts help maximize the grocer’s profit.

  8. Example 2 A school is preparing a trip for 400 students. The company who is providing the transportation has 10 buses of 50 seats each and 8 buses of 40 seats, but only has 9 drivers available. The rental cost for a large bus is $800 and $600 for the small bus. Calculate how many buses of each type should be used for the trip for the least possible cost.

  9. Example 2 A school is preparing a trip for 400 students. The company who is providing the transportation has 8 small buses of 40 seats each and 10 big buses of 50 seats each but only has 9 drivers available. The rental cost is for $600 for the small bus and $800 for a large bus . Calculate how many buses of each type should be used for the trip for the least possible cost. X = Small Buses Y = Big Buses Big Buses (0,9) (9,0) (0,8) (10,0) Small Buses

  10. Example 2 A school is preparing a trip for 400 students. The company who is providing the transportation has 8 small buses of 40 seats each and 10 big buses of 50 seats each but only has 9 drivers available. The rental cost is for $600 for the small bus and $800 for a large bus . Calculate how many buses of each type should be used for the trip for the least possible cost. X = Small Buses (0, 9)Using Cover Up Y = Big Buses Big Buses (0, 8)Using Cover Up (5, 4) Using Elimination Small Buses

  11. Example 2 A school is preparing a trip for 400 students. The company who is providing the transportation has 8 small buses of 40 seats each and 10 big buses of 50 seats each but only has 9 drivers available. The rental cost is for $600 for the small bus and $800 for a large bus . Calculate how many buses of each type should be used for the trip for the least possible cost. X = Small Buses Y = Big Buses $6400 $7200 $6,200 The school should rent 4 large buses and 5 small buses for the least possible cost of $6200

More Related