Discuss the similarities and differences between the different types of LP (linear programming) problems.
Similarities
The first similarity between the different types of Linear Programming problems is the linearity trait. As the name suggests, linear programming problems are linear to allow variables to relate to each other (Thie & Keough, 2011).
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All LP problems are optimization problems. The main purpose is usually to minimize or to maximize some value.
All LP problems have an objective function. This is a function written in terms of the variables which can be changed at will.
Differences
Some LP problems like the graphical method can only be used to solve problems with two variables whereas other methods such as the simplex method can be used to solve more than two variables.
Differences occur in the selection of entering and leaving variable. Other problems look for the maximum positive value while others look for the most negative value column to select the entering variable.
What are the assumptions and requirements to formulate and use an LP model?
The assumption of proportionality. LP problems assume that any change in the constraint inequalities will result in a proportional change in the objective function i.e. if an item contributes $10 toward the profit, the total amount of contribution would be 10X 1 , knowing X 1 to be the number of produced units.
Additivity assumption. This assumption states that the objective function profit is determined by the sum of individual profit contributed by each product separately.
Certainty assumption. The model basically assumes that variables responses to the values are equal to the coefficient responses.
Non-negativity requirement. The LP problem requires that the decision variables assume non-negative variables. This is true since the values of the output cannot be negative (Thie & Keough, 2011).
Discuss how a real-world LP problem in your workplace can be solved using Excel. How does Excel make it easier to solve?
Excel can make it easier to solve a real-world problem since solving LP problems in spreadsheets gives equations for minimizing or maximizing profits. LP involves the objective formula and includes a series of formulas, for instance, one that has the number of needed hours to manufacture the items stated in the objective function. The Excel solver add-in can be helpful as it provides a simple way of solving such problems with numerous formulas. It works backward and finds optimal values to the constraints entered.
Reference
Thie, P., & Keough, G. (2011). An Introduction to Linear Programming and Game Theory . Hoboken: Wiley.
