Question

1.Define what a linear program/linear programing model is including its three key characteristics. Be sure to state those characteristics fully.

2.Some models are deterministic while others are stochastic. Discuss two key differences between deterministic models and stochastic models. Then further demonstrate your understanding of these two different kinds of models by providing an example of a stochastic model including at least two input variables and an example of a deterministic model including at least two input variables.

3.Every linear program/linear programming problem can have one of three possible model solutions. List each of these and then explain how each solution is fundamentally and distinctly different from the others.

4.What is a model constraint? Define it and then discuss a constraint's possible values in any linear program.

5.In the process of transforming model inputs into output, there are two basic types of inputs. List both of these and then discuss in detail how they are very different from each other. Be sure to explain how each of these two different types of input fit into or relate to a model, including the model's objective function.

6.What is the range of optimality? How does it relate to controllable inputs?

7.What is sensitivity analysis and how does it relate to a linear program's solution?

8.What is a maximization linear program? Provide your own example of a linear program that seeks to maximize profit. Be sure to provide some controllable and uncontrollable inputs as well as some constraints and necessary figures (numbers, $, etc.)

9.As part of their work, managers may choose to use a qualitative or quantitative approach in their decision-making process. List at least three reasons why a manager would choose a quantitative approach.

10.Discuss the fundamental relationship between the 7-step problem-solving approach and the 5-step decision-making process.

Answer 1

1. Linear programming is a mathematical method to find out the best possible outcome or solution for a given set of requirements, which are in linear form. Here the best possible outcome is required to maximize profit or minimize the cost. Linear programming is also known as linear optimization because linear programming is mainly used to find the most optimized solution for a set of parameters.

A linear programming model includes one objective function which is a linear equation that must be maximized or minimized. It also includes a set of linear inequalities or constraints.

  
Characteristics:

1) Objective function: All linear programs have an objective function, written in terms of variables that can be changed as per the situation. The objective function is a linear equation which needs to be maximized or minimized.

2) Constraints: All linear programs have constraints inside the objective function. These constraints are written in the form of inequalities, for example, a<4 where a may represent the number of classes taken by a teacher per day. Inequalities determine how the objective function can be maximized or minimized.

3) Linearity: The variables in a linear program must be linear, i.e., there must be proportional relationship between two or more variables.