Linear Programming Concept Paper

1. The Two Types of Linear Programming Discussed.

There were two types of linear programming (LP) that were studied in week five. The first was the graphical method. This method is considered by most to be the easiest way to solve a LP problem. This method can only be used when there are two decision variables; this is because it is not possible to plot the solution on a two dimensional map. Finding the optimal solution in this method is done by plotting the constraints on a graph. The optimal solution is the point that is lying in the region that produces the highest profit. The other method of linear programming is the Simplex method. This method is a repetitive procedure that solves linear equations step-by-step until the optimum solution is reached or the solution is infeasible.

2. Five Examples of LP Applications

Linear programming can be used to solve several different issues that a manager might face; for example, in order to minimize the number of employees, a manager could develop a work schedule that would keep the current level of staffing needs while minimizing the number of employees. Another minimization example is, if there is an ingredient that is going to expire, what is the lowest cost that this ingredient can be used up. Sometimes managers might have limited access to resources so they need to find out which products and at what quantities they need to produce in order to maximize profits. This is often called a production-mix decision. The feed-mix problem is used by feed lot managers to determine the amount of feed to buy in order to meet minimum standards and minimize feed costs. In some situations such as bank tellers, there is a requirement for extra staffing during peak hours. Linear programming is a great way for managers to solve these types of labor scheduling problems.

3. Four Requirements for LP Problems

There are four requirements to develop a linear programming problem. The first is an objective to minimize or maximize some type of quantity. The second requirement is a constraint like the maximum capacity of a machine; there also needs to be alternatives to select from. Lastly, there need to be linearity; if the system is linear, it can be solved through linear algebra.

4. ISO Profit Solution Method

One of the fastest ways to solve linear problems is by using the ISO profit solution method. Just by drawing a series of parallel lines, the solution can be found quite easily. The line that still touches the highest point in the feasible region of the graph will represent the highest profit.

5. Corner Point Solution Method

Another way of solving linear programming problems is using the corner-point method. The highest profit will be in the most extreme point the