# Northeastern University Linear Programming Responses

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### Northeastern University Linear Programming Responses

**I**need two comments, each part is around 100 words.

PART 1;

Linear programming (LP) is used in many aspects of the business because it allows users to break down a variable such as manufacturing costs into smaller components in order to identify where the biggest drivers are to save money or maximize profits. It “helps businesses optimize complex operations by depicting the various solutions in a simplified way” (Pondent, 2018). Let’s say, for example, that you have 50 square feet of office space to use for storage. Your budget is $200, and there are a variety of cabinet types and sizes from which to choose. How do you optimize the space you have available, and stay within the allotted budget? Linear programming is a mathematical technique that determines the best way to use available resources. Thus, I think the biggest advantage of using LP is that this process to help make decisions about the most efficient use of limited resources – like money, time, materials, and machinery.

Another huge benefit to LP is that you can also have numerous constraints. Looking at the manufacturing sector again, this is important because it may not always be a dollar constraint, it may be time-sensitive or limited to certain machinery. Manufacturing takes raw materials and turns them into viable products that can earn the company revenue. However, if any bottlenecks exist, they must be addressed urgently to build the most efficient model (Dotson, 2018). A real-world example of this exists in the manufacturing of medical devices because not only are raw materials and costs a constraint, the finished goods must also be sent to a sterilizer before they can be packaged and sold. It’s often expensive to have your own sterilizer so many companies outsource this to other facilities. Yet there’s risk if all the products are going to the same company to be sterilized… what if there’s a hurricane that shuts down the business? What if they can’t keep up with demand and start developing longer lead times?

This equation would ultimately be designed to maximize profits while minimizing risk and manufacturing costs. Another important term to understand is slack. Slack is basically the unused inputs of the equation (Evans, 2013). For instance, if we had purchased $10,000 in raw materials and spent another $5,000 in labor/processing to produce 100 units that were sent to the sterilizer but not able to get sterilized, the slack here would be $15,000 in the unsalvageable product. Obviously, the business would want to minimize this as well.

In linear programming problems, the shadow price of a constraint is the difference between the optimized value of the objective function and the value of the objective function, evaluated at the optional basis, when the right-hand side (RHS) of a constraint is increased by one unit. For maximization problems like this one, the constraints can often be thought of as restrictions on the number of resources available, and the objective can be thought of as profit. Then the shadow price associated with a particular constraint tells you how much the optimal value of the objective would increase per unit increase in the number of resources available. In other words, the shadow price associated with a resource tells you how much more profit you would get by increasing the amount of that resource by one unit. (So “How much you would be willing to pay for an additional resource” is a good way of thinking about the shadow price.)

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