Title 2nd stats ch 08.pdf ✅

Chapter 8 Operation Research One and Two Marks Questions and Answers Question 1. Define Operations research Answer: “It is the method of application of scientific methods, techniques and tools to problems involving the operations of a system, so as to provide those in control of the system with Optimum solutions to the problem.” Question 2. Mention a method of solving Linear Programmings Problems Answer: Graphical method. Question 3. Define L.P.P Answer: Linear programming is a mathematical technique, which deals with the optimization (Maximization or Minimization) of activities subject to the available resources. Question 4. Mention two areas where the economic operations research can be applied/Uses of Oprations of Research Answer: Linear programming problems are used in Industries for effective use of men, machine, money and Material. Game theory is applied in conflicting situations, to suggest the best strategy. Replacement Problems helps in suggesting the best time period to replace a specific part in manufacturing process, and Inventory problems help in organizing stocks and maintaining costs, and so on. Question 5. Define a solution for a LPP? Answer: A set of real values X = (x1 x2, x3, ...xn), which satisfies the constraints AX(≤ = ≥)b, is called a Solution.
Chapter 8 Operation Research Question 6. What is a feasible solution in a L.P.P? Answer: A set of real values X = (x1, x2, x3, ....... xn), which satisfies- • The constraints AX(≤ = ≥)b and • The non-negativity restriction x > 0 Question 7. Define optimal solution in an L.P.P. Answer: A set of real values X = (x1, x2, x3, ...xn), which satisfies, • The constraints AX(≤ = ≥)b • The non-negativity restriction x ≥ 0 and • Optimizes the objective function Z = CX is called optimal Solution OR If a feasible which optimizes the objective solution Z = CX is called optimal solution Question 8. Define Multiple Optimal solution in LPP. Answer: An LPP is said to have Multiple Optimal Solution if has more one Optimal Solutions. Question 9. When unbounded solution exist for a given L.P.P? Answer: For some LPP the optimum value of Z may be infinity, then LPP is said to have unbounded solution. Question 10. When an L.P.P is said to have no solution? Answer: In a LPP if all the constraints cannot be satisfied simultaneously then there exists no solution Question 11. Why the feasible solution can exists only on xy-plane / Why the solution to the LPP lies in the first Quadrant? Answer:
Chapter 8 Operation Research For the given LPP, the solution can exists only on xy-plane, because of the non-negativity restrictions, x and y both are positive on xy-plane Question 12. In an L.P.P objective functtin is Max Z = 20x + 70y and if solution are A(0,8) and B(12,5). Find optimal solution. Answer: ZA = 20(0) + 70(8) = 560; and ZB = 20(12) + 70(5) = 590 (max) ∴ Optimal soplution is at B(12,5); is x = 12 and y = 5 Question 13. Is an optimal solution always a feasible solution? (In L.P.P) Answer: Yes Question 14. Define/ what is a game? Answer: ’’Whenever there is a situation of conflict and competition between two or more opposing teams, We refer to the situation as a game” Question 15. Write any two properties of a Game/Rectangular Game Answer: 1. there are finite numbers of players 2. Each player have finite number of courses of action OR The game is said to be played, one of the player should adopt one of course action while playing the game. Question 16. Define/Explain /What is meant by a rectangular game/2-person zero-sum game?. Answer: In a game of two players, the gain of one player is the loss of the other. Question 17. Define ’strategy’ in a game. Answer: The strategy of player is the predetermined rule by which he chooses his course of action while playing the game
Chapter 8 Operation Research Question 18. Define the term pure strategy Answer: While playing a game, the pure strategy of a player is the predetermined decision to adopt a specified course of action irrespective of the course of action of the opponent Question 19. What do you mean by a mixed strategy in 2-person-zero-sum game? Answer: While playing a game, mixed strategy of a player is his pre-decision to choose his course of action according to certain pre-assigned probabilities Question 20. Explain the maximin and Minimax of the game Answer: • Maximin is the maximum of row minimums of the payoff matrix, (α) • Minimax is the minimum of the column maximums of the payoff matrix (β) Question 21. What is a saddle point? Answer: Saddle point is the position where Maximin and Minimax coincide Question 22. What is the Principle of Dominance? Answer: If the strategy of a player dominates over the other strategy in all conditions, then the latter Strategy can be ignored, because it cannot affect the solution in any way. Question 23. In a two person zero-sum game, the value ν = -1, is the game fair? Answer: The game is not fair, (the game is said to be fair if ν = 0) Question 24. What is meant by pay-off in a rectangular game?
Chapter 8 Operation Research Answer: It is the gain or loss of the players while playing a game. Question 25. In a game if ν = 2 then what are the values of α & β? Answer: Here α – Maximin and β – Minimax are equal and are equal to ν = 2. Question 26. In a rectangular game, the gain of player – A is 5. Then what is the Gain/Loss of the other player – B? Answer: Loss = – 5 Question 27. Calculate E.O.Q Given D/R = 5000 units/month, C1 = Rs.lO/month, C3 = Rs.200/ month. Answer: Question 28. In a rectangular game pay-off matrix of player A is: Write down the pay-off matrix of player B Answer: The pay-off matrix of player B is: