İŞLETME KARAR MODELLERİ - Deneme Sınavı - 6

Operations research is an analytical method for the management of organizations that provides mathematical solutions to decision-making problems. There are definitive steps of this approach that make it analytical: 1. Problem definition 2. System analysis for the problem and data gathering 3. Model construction 4. Model solution and testing 5. The decision of implementing the solution. So, the correct answer is D.

In both the objective function and constraints, the contribution of every decision variable is proportional to its value. As a result, proportionality assumption casts out any variable that has an exponent other than 1. Consider a firm that aims to maximize its profits under the constraint of its production costs. In practice, production costs are not the same for different levels of production as higher production lowers costs by the economies of scale. To avoid a violation of the proportionality assumption, some characteristics of real-life situations such as economies of scale must be ignored. That undoubtedly makes the model less reliable. The correct answer is A.

The last assumption is certainty, which means that each parameter of a linear programming model is constant in all conditions. In real applications, factors affecting the decisions are not as stable as they are strictly assumed. In the modeling phase, all these assumptions need to be considered while preserving an acceptable level of similarity between reality and what is realized. The correct answer is C.

The problem is related to the number of workers and therefore it is about manpower planning. The correct answer is A.

The decision variables are The quantities, x1 for bonds and x2 for stocks. The objective function seeks to maximize total yields of the holdings and is thus expressed as Maximize Z = (5 × 0.25)x1 + (10 × 0.50)x2 A constraint of the model reflects the liquidity requirements at the end of the year x1 + 0.8x2 ≥ 80 Another constraint is about the size of the portfolio and related to prices of the securities 5x1 + 10x2 ≤ 1000 Percentage limits of the funds to be invested in stocks should not be less than 20% and more than 40%. That means the money spent on stocks cannot exceed the %40 of the total amount of money spent on both types of security. On the other side, the money spent on stocks cannot drop down under %20. These constraints are 10x2 ≤ 0.40 (5x1 + 10x2 ) 10x2 ≥ 0.20 (5x1 + 10x2 ) Simplified expressions of these are 6x2 – 2x1 ≤ 0 and 8x2 – x1 ≥ 0. The correct answer is B.

In the maximization models, the objective function is alternatively named profit function. The logic behind this is the utmost goal of maximizing something is to gain a benefit or a “profit”. The correct answer is D.

In the minimization models, the objective function is alternatively named cost function. The reason for this is the ultimate goal of minimizing something is to reduce loss or “cost”. The correct answer is B.

In the minimization models, draw a line parallel to the objective function and near to the origin. This line should contain at least one point of the feasible region. Find the coordinates of this point by solving the equations of the drawn line and the boundary line(s) of the feasible region. The correct answer is B.

Reality Linear programming is only effective if the model you use reflects the real world. Every model relies on certain assumptions and they may be invalid: you assume, for example, that tripling production will triple sales, but in reality it saturates the market. Linear equations sometimes give results that don’t make sense in the real world, such as a result indicating that you should contract to build 23.75 battleships for the Navy to maximize profits how will you deal with the 0.75 in practical terms? Skilled linear programmers can tweak models and equations to deal with these problems, however. The correct answer is C.

LINEAR PROGRAMMING BASICS

Operations research is an analytical method for the management of organizations that provides mathematical solutions to decision-making problems. There are definitive steps of this approach that make it analytical:

1. Problem definition

2. System analysis for the problem and data gathering

3. Model construction

4. Model solution and testing

5. The decision of implementing the solution

The correct answer is E.

Operations research is an analytical method for the management of organizations that provides mathematical solutions to decision-making problems. There are definitive steps of this approach that make it analytical:

1. Problem definition

2. System analysis for the problem and data gathering

3. Model construction

4. Model solution and testing

5. The decision of implementing the solution

The correct answer is C.

A linear expression appears below; the powers of its variables x and y are equal to one.

2x – 3y

A linear constraint requires a linear expression to be equal to a number, to be less/greater than or equal to a number.

x + y = 4

x – 3y ≤ 2

x ≥ y

The last expression stated above is called a non-negativity constraint, which requires the value x to be greater or equal to zero. A linear program either minimizes or maximizes a linear expression subject to defined linear constraints. The correct answer is E.

An objective function is the function of a linear programming model that is desired to be maximized or minimized.

The correct answer is D.

The foundation of operations research is mostly cited to studies and applications in the U.S. Army right before The World War II. However, LeonidV. Kantorovich is recognized as the first to explore this area. In 1939, Kantorovich published a paper on a method for a production plan which he claimed to be the optimal way. This study included a linear program without a systematic solution. The systematic solution which is called “simplex algorithm” was later introduced by George B. Dantzig, who had planning experience in the U.S. Army Air Force. Tjalling C. Koopmans, who built a model for ship routes, was another contributor to the field. He and Kantorovich shared 1975 Nobel Prize in economics for their studies on the optimal allocation of resources. The correct answer is D.

x ≥ y

The last expression stated above is called a non-negativity constraint, which requires the value x to be greater or equal to zero. A linear program either minimizes or maximizes a linear expression subject to defined linear constraints. The correct answer is C.

An optimal solution is a feasible solution that reaches the most favorable value of the objective function. The correct answer is B.

The last assumption is certainty, which means that each parameter of a linear programming model is constant in all conditions. The correct answer is B.

Either it is the objective or the constraints, every function is the sum of the individual contribution of the respective variables. This is called the additivity assumption, which prohibits cross-product terms in the expressions of a linear program. This assumption restricts the model design as well.

The correct answer is B.

Proportionality assumption casts out any variable that has an exponent other than 1. The correct answer is A.

In a decision problem, occurrences are chance occurrences and all the chance occurrences are governed by probabilities. In the decision making with probability information, a strategy matrix is created and the best results are determined. Another approach used to solve such decision problems is the decision tree. A decision tree is a graphical approach that helps decision-makers see all the scenarios they may encounter. The correct answer is A.