How to Solve Linear Programming Word Problems | Maximization and Minimization

In this lesson, we are going to discuss how to solve linear programming word problems. Linear programming (LP, also called linear optimization) is a method to achieve the best outcome such as maximum profit (maximization problem) or lowest cost (minimization problem) in a mathematical model whose requirements are represented by linear relationships. We are going to discuss the following: Maximization Problem Consider a chocolate manufacturing company that produces only two types of chocolate – Milk Chocolate (M) and Extra Creamy Chocolate (E). Both the chocolates require milk and chocolate only.  To manufacture each unit of M and E, the following quantities are required: Each unit of M requires 1 unit of milk and 3 units of chocolate. Each unit of E requires 1 unit of milk and 2 units of chocolate. The company kitchen has a total of 5 units of milk and 12 units of chocolate. On each sale, the company makes a profit of Php 6.00 per unit M sold, Php 5.00 per unit E sold. Now, the company wishes to maximize its profit. How many units of M and E should it produce respectively? Minimization Problem A cargo-forwarding firm is planning a major fleet expansion and will purchase a maximum of 15 new trucks. These vehicles are supposed to provide at least 36 tons of additional load capacity. One model holds 2 tons and costs Php1.5M. A second model holds 3 tons and costs Php2.4M. How many trucks of each model should the firm purchase to provide the additional load capacity of minimal cost? What is the minimal cost? ⏲️ Timestamps ⏲️ Introduction (0:00) What is linear programming (0:50) Basic Components of Linear Programming (1:10) Linear Programming Word Problem 1 (1:28) Linear Programming Model Formulation (2:50) How to find the feasible region using Geogebra (8:04) Linear Programming Word Problem 2 (16:16) Linear Programming Model Formulation (16:57) How to find the feasible region using Geogebra (19:13) WANT TO WATCH MORE VIDEOS LIKE THIS? 📺 Subscribe to my channel here: http://bit.ly/mathhubtv CONNECT WITH US 👍 Facebook: https://www.facebook.com/mathhubtutorials 🐦Twitter: https://twitter.com/mathhub303 NEED PERSONAL ONLINE TUTORIALS? Contact us at [email protected] 🙋‍♂️ Have questions? I'm here to help you learn your math courses in an easy way. Leave a comment below and I will try to answer it as soon as I can. You can also leave topics that you need help with and I will create those videos for you.