greatest in columns : 2 6 7 3 ; min : 2. pg. 151. Correct answer is A.

One of the special kinds of stochastic processes is Markov Chains. Markov chains have a special property that probabilities indicating how the process will evolve in the future depending only on the present state of the process, and so are independent of events in the past. In stochastic processes, events occur over time, and time can be dealt with either in discrete fashion or continuous fashion.

The answer is option A, I-II-III-IV.

A rational player never plays a dominated strategy.

lowest in rows : -2 -6 -4 ; max : -2 ; greatest in columns : -1 1 ; min : -1 ; sum = -2 + -1 = -3 . pg. 151. Correct answer is D.

Max -Z = -x₁ - 3 x₂ - 2 x₃ - 5 x₄ - 4 x₅ ; no positive coefficient ; x₁ : it has the maximum negative coefficient . pg. 95 . Correct answer is C.

A transition matrix is called regular if some power of the matrix includes all positive entries.

The solution of a transportation model follows three steps to reach the optimum. First step is to determine a basis, which is the initial basic feasible solution. The next step is to check the optimality of the solution. The third step is conditional to the second: if the current solution is not optimal, then the process is to iterate to a new basic feasible solution that includes the entering variable determined in the previous step. The correct answer is A.

The steps of Hungarian Method is given below.
1. Identify the smallest value of each row for the cost matrix of the assignment problem. Subtract each row’s smallest value from all the costs in the respective row.
2. Identify the smallest value of each column for this altered matrix. Subtract each column’s smallest value from all the costs in the respective column.
3. Mask the columns and rows out that have a zero value. The number of masked out rows and columns must be at a minimum.
4. If the number of masked out rows and columns is equal to n, then the optimum can be obtained from the present matrix; move on to the next step. If not, skip to Step 6.
5. Identify the optimal solution by the coordinates of the zero-valued elements in the present matrix.
6. Identify the smallest value except for the ones in masked out rows and columns. This value is then subtracted from the values of unmasked rows and columns and, added to the intersections of masked out rows and columns. Return to Step 3.

According to these, the correct answer is given in option C.

The optimum basic feasible solution has basic variables given below

x₁₃ = 1, x₂₅ = 1, x₃₄ = 1, x₄₂ = 1, x₅₁ = 1

The lowest cost of the assignments is 110 TL.

Z = 1 × 30 + 1 × 50 + 1 × 15 + 1 × 15+ 1 × 0= 110 TL.

Strong duality property refers that the objective value of Z and the objective value of W are equal only if the basic feasible solution is the optimal for the primal as well as the dual model. In the equation below, the asterisk denotes that x and y are the optimum feasible solutions. cx* = Z = W = y* b. The correct answer is D.

A game is defined to be any situation in which
• There are at least two players,
• Each player has a finite number of strategies,
• Each player’s chosen strategies determine the outcome of the game,
• Each player acts rationally to maximize his/her gains,
• The different strategies of each player and the amount of gain is known to each player in advance.

This method is based on opportunity loss, also called regret. It is defined as the difference between the optimal and the actual pay-off. Regret is the amount lost when the best alternative is not selected.
This method proposed that maximum regret be minimized by choosing the best pay off for each event. The regret of each event for each alternative is calculated and regret matrix or opportunity loss table is created. This table shows the losses to be incurred if the alternative is not selected for the best outcomes of each event.
If the objective is maximization, the maximum value of each event is determined. All values of the relevant event are subtracted from this maximum value. If the objective is minimization, the minimum value of each event is determined. The smallest value of each event is subtracted from all values of relevant event. In this way, the regret matrix is obtained.
After the regret matrix has been constructed, the maximum opportunity loss (regret) for each alternative is located. Then the alternative with the smallest value
among these maximum regrets selected.

In this method, regardless of the objective function, the smallest value is always selected from the regret matrix.

According to these information, the correct answer is given in the option C.

The Odds and Evens Game: In this game, two players (called Odd and Even) show simultaneously either one finger or two fingers. If the sum of the fingers put out both players is odd, the Odd wins $1 from the Even. If the sum of the fingers is even, the Even wins $1 from the Odd.

If two corner-point feasible solutions are connected by a line segment, these cornerpoint feasible solutions are adjacent. Two corner-point feasible solutions are adjacent if all but one of their respective variables have the same value.

The correct answer is B.

The simplex method concurrently identifies basic feasible solutions for a primal model and its dual. This is a property of the duality called complementary solutions property. This property allows checking for the optimality of the primal solution by inspecting the feasibility of its dual solution.

A1 : x1 = (100 – 50) (0.3) + (110 – 110) (0.5) + (60 – 30) (0.2) = 15 + 0 + 6 = 21 ; A2 : x2 = (100 – 100) (0.3) + (110 – 60) (0.5) + (60 – 50) (0.2) = 0 + 25 + 2 = 27 ; A3 : x3 = (100 – 70) (0.3) + (110 – 90) (0.5) + (60 – 60) (0.2) = 9 + 10 + 0 = 19 . pg. 37 . Correct answer is A.

A pure strategy is an unconditional decision always to select a particular course of action. For example, in the game of Rock-Paper-Scissors, if a player would choose to only play Rock for each interdependent trial, regardless of the other player’s strategy, it would be the player’s pure strategy.