Questions
Question 1
Linear Programming is a problem-solving tool that applies mathematical models that are linear in planning activities for certain decisions. It is applicable in almost all forms of organization in both for-profit and not-for-profit organizations. It is also applicable to government entities and institutions. It widely applied where limited resources have to be allocated among various activities that need resources simultaneously.
Question 2
The graphical method can only be used in solving linear programming models with only two decision variables. This is because a simple graph has only one dimension. A one dimension graph has only two axes: x and y. Therefore, only two decision variables can be applied. One will be placed on the x-axis, and the other one will be placed on the y-axis.
Question 3
The axis represents the two decision variables for the problem. For instance, if a firm is interested in producing two goods with limited resources. The two goods will be represented on the axis as the decision variables. One good will be on the x axis and the other on the y axis.
Question 4
The constraint boundary line is a line is a graphical representation of the constraint boundary equation. It shows the restrictions that bind a given problem that needs to be solved. For a maximization problem, it shows the boundary beyond which it cannot be surpassed. For instance, in allocating resources the maximum amount allocated is the resource endowment of the entity. The entity cannot allocate more resources than it owns. Therefore, it is restricted by its resources which will form the constraint boundary. The decision that will be arrived at has to within the space between the intersection of the various boundary lines.
Question 5
The constraint boundary equation is obtained when the inequality sign (greater than or less than) is replaced by an equality sign. Replacing with an equality sign allows the solver to identify points for plotting the constraint boundary line.
Question 6
A feasible solution is one that satisfies all the constraints that bind the decision that is to be made (objective function). It is the area between the intersections of the boundary lines. The solution must all be non-negative. Therefore, is above the x-axis and to the right of the y-axis. Only solutions that are within this area can be achieved in light of the constraints the firm faces.
The optimal solution shows the results that can be achieved given the objective function that the firm seeks to satisfy. The objective function is the decision problem that the firm seeks to address. Therefore, the optimal solution gives the best solution for the decision problem given the constraints. Since the feasible areas show all possible solutions that are achievable, the optimal solution has to be within the feasible solution area. In other words, the optimal solution is a sub-set of the feasible solution.
Question 1
Possible states of nature are all the plausible events that can occur. It is applied in decision making where there is uncertainty. The person making the decision is not sure what will happen because there are more that event that can occur. For instance, if we consider the possibility of raining, there are two possible states of nature. That is, it either rains, or it does not rain.
Question 2
Prior probabilities refer to when the decision maker has some information about the likelihood of the possible events based on experience or institution of the decision maker as a subjective judgment or it may be from hard evidence obtained through research or another factual basis.
Question 3
Question 4
The maximax criterion ignores the prior probabilities for the events. Therefore, it may result in selecting decisions with a very limited chance of success which may be detrimental. It only considers the best events by assuming that it is the only one that will occur. Unfortunately, both events are likely. Therefore, if the worse alternative occurs, the firm may make significant losses.
Question 5
The maximin criterion also ignores the prior probabilities for the events. Therefore, it may result in selecting decisions with the belief that the worst outcome will happen. It only considers the worst events assuming that it is the only one that will occur. Unfortunately, both events are likely. Therefore, if the firm may leave out good projects that would have resulted in better pay off for projects whose pay off are just average.
Question 6
The Bayes method is often criticized on the basis that it assumes that prior outcomes are known. In most cases, it is difficult to predict probabilities with certainty as there are many factors that can influence an outcome. Bayes method may also not be applicable in a situation where past probabilities are not known since the event is new. For instance, the probability of electing a woman president in the USA. It is not known since it has never happened in the past. In this case, the Bayes method cannot be applied. The Bayes method is also complex. Most people do not understand the method and also find it difficult to apply it in practice. In organizations, there are decision makers from various backgrounds. Someone who does not have a good mathematical background may find it difficult to understand a decision made using Bayes. Therefore, the applicability of the theory is limited to those with a mathematics background.
