Each week, you will be asked to respond to the prompt or prompts in the discussion forum. Your initial post should be a minimum of 300 words in length, with citation and is due on Sunday. By Tuesday, you should respond to two additional posts from your peers By Tuesday, between 75-150 words.

**Linear Programming Models**

Please refer to this example for a real world application of LP model by FedEx Company. (https://www.analyticsvidhya.com/blog/2017/02/lintroductory-guide-on-linear-programming-explained-in-simple-english/)

Can you find another good real world application of LP model and discuss the similarities between them (target functions, constraints, etc.)?

**Alyssa Gutwein **

It was difficult for me to find another specific real-world example of linear programming applied to an actual business like the FedEx example, so instead I found an example that explains how the restaurant industry might use linear programming on a daily basis (found in the link “How do restaurants use linear programming for menu planning?”). This example discusses how the first step in any linear program equation is determining the objective, and in this case the objective is how many of a menu item the restaurant should prepare to meet demand and stay within budget at the same time (Perez, 2017). The goal is to maximize the number of meals able to be prepared with limited amount of produce/ingredients. The next step is to identify the constraints such as the budget for the day which must be kept in order for the restaurant to turn a profit. Using this information and a linear programming model, restaurants can determine how much of each menu item they are able to prepare and still stay within budget. This is the same concept and formulation used in the FedEx example. The delivery driver used linear programming to determine the best solution to his problem (getting all packages delivered in the shortest amount of time/distance possible). Once the objective was determined (delivering all packages in shortest amount of time) and the constraints were identified (limited time and gas), the delivery driver could calculate a formula using these numbers to find the best solution to the problem. This is essentially the same as the example about the restaurants where there was an objective that needed to be identified and solved for and constraints that had to be considered.

Kashyap, S. (2019). Introduction to Linear Programming and Optimization in Simple English. Retrieved from http://www.analyticsvidhya.com/blog/2017/02/lintroductory-guide-on-linear-programming-explained-in-simple-english/

Perez, D. (2017). How Do Restaurants Use Linear Programming for Menu Planning? Retrieved from https://smallbusiness.chron.com/restaurants-use-linear-programming-menu-planning-37132.html

**Nina Hahn **

LP has many applications in practice. A similar application to the Fed Ex example is mixing problems where the aim is to combine ingredients into an end product, where the amount of each ingredient can be varied within a certain range. An example of this is the diet problem George Dantzig studied in 1947: a number of raw materials (e.g. oats, pork, sunflower oil etc.) are given together with their content of certain nutritional values (e.g. protein, fat, vitamin A etc.) and their price per kilogram. The task is to mix one or more end products from the raw materials at minimal cost, subject to certain minimum and maximum limits for the individual nutritional values. Such mixing problems also occur during melting processes, e.g. in steel production.

Target functions of both examples are very simlar because both try to work out the smartest way, Fed Ex to deliver packages and the mixing example to have all needed products at the same place in time. Both companies will try to optimize their supply chain to save money and to use their employees most efficiently. Both companies also work on optimizing the delivery route. With the help of clustering and greedy algorithm the delivery routes are decided by companies. The objective is to minimize the operation cost and time. As it is written in the example of FedEx: ” Their motive is to maximize efficiency with minimum operation cost. As per the recommendations from the linear programming model, the manufacturer can reconfigure their storage layout, adjust their workforce and reduce the bottlenecks”.