The alpha coefficient is determined by the decision maker as 0.3. Then 1-alpha becomes 0.7. In this case, the decision maker is optimistic with a probability of 30%, and pessimistic with a probability of 70%.

First, the minimum values are determined for each alternative. These values are multiplied by the α coefficient. Then the maximum values are determined for each alternative. These values are multiplied by the (1- α) coefficient. These values of each alternative are sum up.
Product 1 = 3*0.3 + 12*0.7 = 9.3 days
Product 2 = 1*0.3 + 18*0.7 = 12.9 days
Product 3 = 5*0.3 + 15*0.7 =12 days
Product 4 = 4*0.3 + 11*0.7 = 8.9 days
Product 5 = 2*0.3 + 10*0.7 = 7.6 days
Then, because the objective is minimization the lowest value (7.6 days) and the alternative for that value (Product 5) is selected.

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”. In the maximization models the value of Z needs to be increased as much as possible. An infinite number of iso-profit lines can be drawn for increasing values of Z. However, under the constraints of the model, the highest possible value of Z must reside in the feasible region.

As also understood from the information given, the statements in the options I, II and IV about the maximization models are correct, so the correct answer is D. The statement in the option III is not correct because of the fact that an infinite number of iso-profit lines can be drawn for increasing values of Z. However, under the constraints of the model, the highest possible value of Z must reside in the feasible region.

The concept of decision making is to choose the most appropriate one among the available alternatives, in other words to make the best choice.The correct answer is 'A'.

For the values given in the Table, a regret matrix is created. Because the objective is
minimization, the minimum value of each event is selected. The smallest value of each event is subtracted from all other values in relevant column. Thus, a regret matrix is created. This table shows the regret matrix of the problem.

According to the results in Table, maximum regret of each alternatives are as follows:
Product 1 = maximum regret = 5 days
Product 2 = maximum regret = 8 days
Product 3 = maximum regret = 6 days
Product 4 = maximum regret = 4 days
Product 5 = maximum regret = 3 days
The alternative with the smallest value (product 5) is chosen among the maximum regrets. The correct answer is E.

The method used for the loss of opportunities when the best alternative is not selected is “Minimax Regret”. This method is based on opportunity loss, also called regret. In this sense the correct answer is option B.

There are some common characteristics of decision making. These are “decision maker”, “objective”, “alternatives (strategies/actions)”, “events (states of nature)”, “outcomes (pay-off)” and “payoff table / pay off matrices.The correct answer is 'B'.

First, the minimum values are determined for each alternative. These values are multiplied by the ? coefficient. Then the maximum values are determined for each alternative. These values are multiplied by the (1- ?) coefficient. These values of each alternative are sum up.

Among these values, the lowest is 4.80, and this belongs to A1.

A1 = 2*0,6 + 9*0,4 = 4,80

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.

In decision making at risk, the expected value criterion is commonly used when comparing alternatives. And when the decision’s consequences involve only money, we can calculate the Expected Monetary Value (EMV).

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

When the decision have information about the probabilities of occurrence of the events, the decision making environment is called “decision making under risk”.The correct answer is "B".

In criterion of optimism (plunger), the best outcome for each alternative is realized and decision maker select the best among these alternatives.

In a decision problem, the decision maker is aware of various possible events (states of nature) but has insufficient information to assign any probabilities of occurrence to them. This kind of a decision problem is termed as decision making under uncertainty. There are many unknowns and no possibility of knowing what could occur in the future to change the outcome of a decision in decision making under uncertainty.
For firms launching a new product, an important change in marketing strategy or opening first branch can be given examples of decision making under uncertainty.

In the context of the above explanations, the correct answer is C.

In decision making under risk, there exist more than one state of nature and the decision maker has sufficient information to assign probabilities to the occurrence of each of these states. The probabilities can be obtained from past records or the subjective judgment of the decision maker. In other word, decision situations in which the chance of occurrence of each state of nature is known or can be estimated are defined as decisions made under risk.

han one state of nature and the decision maker has sufficient information to assign probabilities to the occurrence of each of these states. The probabilities can be obtained from past records or the subjective judgment of the decision maker. In other word, decision situations in which the chance of occurrence of each state of nature is known or can be estimated are defined as decisions made under risk. Such decision-making problems are also known as probabilistic or stochastic decision problems. The correct answer is D.

The modeling phase is the transformation of verbal description of the problem into a mathematical model under the linear programming assumptions. This model is a system of equations and inequalities representing the objective and the constraints. The decision to be derived from the model is related to quantifiable variables that are in control. These variables of decision x₁, x₂, ... , x_n and the constants (i.e. the coefficients and right-hand side values of the inequalities) are called the decision variables and the parameters respectively. The objective function (for example, Z= 2x₁ + x₂) is an appropriate measure of performance for the problem. It can be maximized or minimized depending on the desired achievement. Finally, a constraint is a restriction on decision variables by means of equality or inequality (for example, 5x₁ + 6x₂ ? 30). As also understood from the information given, the statements in the options I, II and III are correct, so the correct answer is C. The statements in the option IV and V are not correct because of the fact that These variables of decision x₁, x₂, ... , x_n and the constants (i.e. the coefficients and right-hand side values of the inequalities) are called the decision variables and the parameters respectively.

In decision making under risk, decision makers have information about the probability of occurrence of each events. The probability value can be known precisely or predicted. These possibilities can be obtained from the personal opinions of the decision-maker, from the statistical records held in the enterprise, from expert opinions, from market research.