(a) Define the slack and surplus variables. What do they represent? What is (are) the difference(s) between a slack and a surplus variable? Give one real-world example for each. (6) What are the different types of special situations that may occur while solving a linear programming problem? Briefly describe each of these special situations and give one real-world example for each special situation. What are the different methods to solve a system of linear equations? Briefly describe the steps needed in each method. Briefly describe the important parts of each step needed to make a decision using decision sciences models.
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(a) Slack variables are variables added to a linear programming problem to convert inequalities into equalities. They represent the amount of unused resources in the problem. Surplus variables, on the other hand, are variables added to a linear programming problem Show more…
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The development of linear programming is perhaps among the most important scientific advances of the mid-20th century. Today, it is one of the standard tools that has saved many millions of dollars for most companies and enterprises. Identify at least two reasons for the importance of linear programming in an enterprise of your choice and describe the impact that linear programming has had in that enterprise in recent decades. Provide a specific example of a linear programming model related to the enterprise that you have selected and interpret the slack variables of your example. Describe how the information obtained about the slack variables of your example can be used by the decision-making sector of that enterprise. (You do not have to write a mathematical formulation of your example. Simply mention the objective, the decision variables, and a few possible constraints to describe your model example).
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