For this system of equations, basic solutions can be determined by setting two (n – m = 2) of the variables to zero and solving the equations for the remaining two (m = 2). 

The correct answer is C.

The simplex algorithm iteratively switches to the next basic feasible solution that is adjacent to the previous basic feasible solution until it reaches the optimum Z.

A state is called periodic, if it can only return to itself after a fixed number of transitions greater than 1.

lowest in rows : 5 7 ; max : 7 ; greatest in columns : 15 7 10 ; min 7 ; max min : 2nd row , 2nd column . pg. 164. Correct answer is A.

A state i of a Markov chain is called an absorbing state if, once the Markov chain enters the state, it locks in there forever.

The assignment model has a tailored solution method such as the transportation model does. The solution method of the assignment model is called the Hungarian Method, named by the nationality of its developers. The steps of Hungarian Method are 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.

The n-step transition probability pij(n) is the probability that a process in state j will be in state i after n additional transitions.

In transportation models, the total supply equals the total demand. Some transportation problems may be less restrictive; the total supply may exceed aggregate demand. In such a case, a dummy destination must be defined to fictionally absorb an excessive amount of the supply. Thus, the model becomes balanced and fits the general form of the transportation model.

The steps of the method for solving m×2 games are as follows:
Step 1. Draw two vertical axes one unit apart. These two lines are 0 and 1.
Step 2. Take the probabilities of the two alternatives of the column player as q and (1-q), then expected pay-offs of row player for each strategy are expressed with equations.
Step 3. These equations are then plotted on the graph.
Step 4. Draw n straight lines for j=1, 2… n and determine the lowest point of the upper envelope obtained. This will be the minimax point.
Step 5. The two or more lines passing through the minimax point determines the reduced 2 x 2 payoff matrix. The optimum solution of the game is obtained as in 2 x 2 game.

If the solution is optimal, then we stop the process.

If the value of a game is zero, then it is called a fair game

Once state V is entered, it is impossible to leave from it. For this reason, state 2 is an absorbing state. The answer is E. 

Familiar examples of stochastic processes are as follow:
• daily prices of a stock or exchange rate
fluctuations,
• failures times of a machine,
• medical data such as a patient’s blood
pressure or EKG,
• radar measurements for the position of an
airplane,
• toss a coin

A transportation problem is a linear optimization problem, which seeks to minimize the total transportation cost from the origins to the destinations. The total cost is the sum of the total cost of each route, which is the multiplication of the unit cost with the amount of the units to be transported on the respective route. The decision variables of this problem are the amounts of shipment, as the transportation costs are given data. A balanced transportation model is a linear model with equality constraints. The inverse of a linear problem can be modeled as the dual of the original model. The dual of a balanced transportation problem is interpreted as a problem of a counterpart who provides an alternative to transportation. The decision variables of the dual model are the prices of the alternative service offered by the counterpart actor. At the optimum point, the objective value of the primal and the dual models are the same, and the optimum solution is the only solution that meets the restrictions for both models. Hence, the optimality of a basic feasible solution for the transportation model can be tested by checking the feasibility of the dual solution. The correct answer is B.

The steps of the decision making process are as follows:

1. Define decision problem
2. Establish objectives
3. List all possible decision alternatives
4. Identify the possible outcomes for each decision alternative
5. Identify the pay-off matrix for each combination of alternatives and events
6. Select the most appropriate decision making method and apply this method
7. Determine the best alternative and make your decision

The correct answer is A.

Least-cost Method: The Least-cost method considers the respective costs of the variables so as to find a basic feasible solution that approximates the optimum solution more. Unlike the Northwest Method, the Leastcost algorithm begins with selecting the route that has the smallest unit cost of transportation. If there is more than one variable that has the smallest cost, any variable among these can be selected arbitrarily. The value allocated to the selected route is the greater one of the values of the supply and demand. The satisfied column (corresponding demands) or row (corresponding supplies) is masked out with grey and ignored for the next allocations. Next, subtract the allocation value from the supply and demand and repeat the same allocation process with the remainders of the supply and demand. The process continues until the last row or column is satisfied. The correct answer is C.

The probabilities of going from one state to another are called transition probabilities.

corner point . pg. 87. Correct answer is D.

The coefficients of the variables in the objective function refer to the effect of one-unit increase of respective variable on the function output Z. Hence, these coefficients correspond to the rate of improvements of the respective variables in Z. According to the objective function of the program, increasing x₂ from zero yields more than increasing other variables from zero. Thus, the entering variable is x₂.