New Semester Started Get 50% OFF Study Help! --h --m --s Claim Now

Question Answers

Textbooks

Find textbooks, questions and answers

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Study Help
Tutors
AI Study Planner NEW
Sell Books

Search
Sign In
Register

study help
business
understanding management

Quantitative Techniques In Management 4th Edition N D VOHRA - Solutions

14. All dynamic programming problems call for maximising the given payoff function. Mark the statements as T (True) or F (False).
13. The states of a given stage refer to the various possible conditions in which the system can be in that stage. Mark the statements as T (True) or F (False).
12. Every stage in a dynamic programming problem calls for making a policy decision. Mark the statements as T (True) or F (False).
11. Each sub-problem in a dynamic programming problem is called a stage. Mark the statements as T (True) or F (False).
10. Probabilistic dynamic programming is used where it is not possible to break the given problem into clear cut sub-problems. Mark the statements as T (True) or F (False).
9. In a shortest route problem, the optimal solution indicates the length of most direct route from origin to destination that involves least number of nodes on the route. Mark the statements as T (True) or F (False).
8. Dynamic programming is similar to linear programming in its approach to solving problems. Mark the statements as T (True) or F (False).
7. In dynamic programming, there is a standard algorithm which can be programmed to solve all problems. Mark the statements as T (True) or F (False).
6. BY dynamic programming it is possible to obtain the best and next-best solution to a problem. Mark the statements as T (True) or F (False).
5. The optimal solution to a dynamic programming problem is obtained by solving all stages of the problem sequentiallY. Mark the statements as T (True) or F (False).
4. Dynamic programming problems consist of a series of independent sub-problems. Mark the statements as T (True) or F (False).
3. In dynamic programming, the given problem is solved in stages beginning at the last stage and working backward to initial stage. Mark the statements as T (True) or F (False).
2. A dynamic programming problem consists of multiple smaller problems, known as states, with interconnected decisions.Mark the statements as T (True) or F (False).
1. Dynamic programming is a quantitative analysis technique which is applied to large, complex problems. Mark the statements as T (True) or F (False).
An investor has Rs 10,000 to invest and she has an opportunity to invest the amount in either of two investments A or B, at the beginning of each of the following three years. The investment A results either in a total loss of the amount invested with probability 0.3, or a gain of Rs 10,000 over
Let us suppose that a traveller wants to go from city A to city B. Suppose, further, that the two cities are at a long distance from each other and also that there is no direct link between them. The traveller is, in fact, required to break his journey thrice during the course of his travel. At
11. An absorbing state is one which once reached, does not allow transition to another state. Mark the statement as T (True) or F (False).
25. If a chain begins in a given transient state, t;, the probability that it shall eventually be absorbed in absorbing state a1 would be given by the ijth element of the "fundamental matrix" of the Markov chains. Mark the statement as T (True) or F (False).
1. What do you understand by Markov processes? In what areas of management can they be applied successfully?
2. What do you understand by transition probabilities? Is the assumption of stationary transition probabilities realistic, in your opinion? Why or why not?
3. Distinguish between a recurrent and an absorbing state. How can you tell in a transition matrix as to which states are recurrent and which are not?
4. Discuss the following assumptions in relation to the Markov chains:(i) Finite states(ii) First-order process(iii) Stationarity of transition probabilities(iv) Uniform time periods
5. How are steady state probabilities calculated? Do you agree that they are independent of the initial condition? Explain.
6. Explain how the probability tree helps to understand the problem of Markov processes.
8. Saddle point is the point of equilibrium. Mark the statement as T (True) or F (False).
7. Explain the method of calculation of ending up in each absorbing state when a chain begins in a particular transient state.
8. What is fundamental matrix of Markov chains? What does it calculate?
23. It is true to say that in equilibrium, the state probabilities in periodk, [Q(k)], are the same as the state probabilities in period k- 1, [Q (k- 1)]. Mark the statement as T (True) or F (False).
22. For a Markov process with two states, 1 and 2, transition probabilities as Pu, p 12 , p21 and p 22, the equilibrium probabilities q I and q2 can be obtained by solving the following pair of equations simultaneously:qi = Pu qi + P21 q2 and q2 = P12q1 + P22 q2. Mark the statement as T (True) or F
12. Two states i andj are not communicative ifj is an absorbing state. Mark the statement as T (True) or F (False).
13. In a system, recurrent states are those which are not transient. Mark the statement as T (True) or F (False).
14. In a transition probability matrix, the sum of probabilities for each row and column is equal to 1. Mark the statement as T (True) or F (False).
15. A transition probability equal to 1 in a transition probability matrix indicates an absorbing state. Mark the statement as T (True) or F (False).
16. A market where only three brands of soft drinks are sold and the choice of a particular brand of soft drinks is assumed to depend on the choice in the immediately preceding time period, can be modelled as a first-order Markov process. Mark the statement as T (True) or F (False).
17. The inputs required for Markovian analysis include the transition probabilities and the initial condition in which the given system is. Mark the statement as T (True) or F (False).
18. In a market with four brands of bread, the initial condition described by the vector[0.25 0.25 0.50 0] implies that, currently, the first two brands enjoy an equal share of the market, the third brand has a share equal to the total share of the first two brands, and the fourth brand enjoys
19. The probability distributionofa system being indifferent states 1, 2, ... ,n, at any given time kgives the steady state probabilities, and is expressed as Q(k) = [qi(k) qi(k) ... qnCk)]. Mark the statement as T (True) or F (False).
20. Steady state probabilities are independent of time. Mark the statement as T (True) or F (False).
21. In a Markov chain with three states, 1, 2 and 3, with given transition probability matrix, P, the probability that the system, presently in state 3, shall be in the state 1, three periods from now, would be given by element 3,1 of the matrix P3• Mark the statement as T (True) or F (False).
9. "The Markov analysis may be understood as the way of analysing the past and present movement of some variable in an effort to forecast the future movement of that variable." Explain this statement by taking examples from marketing and personnel. (MBA, Delhi, April, 1998)
10. How can Markov analysis be used by a company to(i) predict its manpower needs;(ii) allocate service department overhead to production departments; and(iii) analyse its accounts receivables.
11. "The Markov chain method analyses the current behaviour of a process and relates the existing characters to the future." Elucidate this statement by taking examples from functional areas of management.
12. There are three firms ABC, PQR and XYZ sharing a market as 40%, 40% and 20% respectively on January 1, 2009. Over a Year, the following developments take place:ABC retains 80 per cent of its customers, loses 16 per cent to PQR and 4 per cent to XYZ.PQR retains 84 per cent of its customers,
13. A company is using Markov theory to analyse brand switching between three different brands of DVDs.Data has been obtained and used to estimate the following transition matrix for the probability of moving between brands each month:The current (i.e. month 1) market shares are 45%, 25% and 30%
14. ABC Co. had 45% of the local market for its cosmetics, while the two other manufacturers XYZ Co.and PQR Co. have 30% and 25% shares, respectively, in the local market, as on 1st January of this year. A study by a market research firm has disclosed the following: every year, ABC retains 80% of
15. A transport company with a large fleet of buses periodically inspects the bearings on its buses and categorises them in one of the four states: (1) Good Bearings, (2) Lightly-worn Bearings, (3) Moderately-worn Bearings and ( 4) W om-out Bearings. Replacement of bearings during inspection costs
16. Formulate alternative Markov chain models for two policies for repairing a piece of equipment that must be finely adjusted. The equipment can be in any of three conditions: running ( or just repaired), running fairly well, and running poorly. If running well, it will continue in that condition
17. A manufacturing company has a certain piece of equipment that is inspected at the end of each day and classified as just overhauled, good, fair or inoperative. If the piece is inoperative, it is overhauled, a procedure that takes one day. Assume that the working condition of the equipment
19. A company has two production departments, P1 and P2 and three service departments, S1, S2 and S3•The direct cost allocated to each of the departments and percentage of total cost of each service department apportioned to various departments are given here:Draft this problem as absorbing
18. ABC company has three service departments, S1, S2 and S3, and two production departments P1 and P2• Overhead is allocated to the production departments for inclusion in the stock valuation. The analysis of benefits received by each department during the last quarter and the overhead expense
20. A holding company Hhas two subsidiaries S1 and S2• The subsidiaries also own a portion of the share capital of H. The percentage ownership of the group is as given below:If the separately earned net profits of H, S1 and S2 are Rs 30,000, Rs 17,500 and Rs 5,000, respectively, find the total
21. A credit card company is attempting to determine a more effective set of credit control policies. It has traditionally classified all its accounts receivables into one of the five categories listed below:Based on the historical data, the company has derived the following transition matrix
11. On January 1 (this year), Bakery A had 30% of its local market share while the other two bakeries B and Chad 40% and 30%, respectively, of the market share. Based upon a study by a marketing research firm, the following facts were compiled. Bakery A retains 85% of its customers while gaining 5%
10. Three business magazines, Business Today, Business Line and Business Life, compete for advertising shares in a city. At the end of last year, Business Today had 40 per cent of the market while its competitors Business Line and Business Life each had 30 per cent of the market. During the last
24. The analysis of Markov chains with n states, out of which mare transient, requires decomposing the transition probability matrix into four sub-matrices: Q ( of the order n - m by n - m) matrix of transient probabilities; R ( of the order n - m by m) matrix of transitions from transient to
1. A person plays a game in which he gains Rs 20 with a probability of0.4 or loses Rs 10 with a probability of 0.6. He has an amount of Rs 20 with him and plays the game repeatedly until he loses all the amount he has or adds Rs 30 or Rs 40 to the initial amount. Draw up a transition probability
35. The matrix below shows the paY-off in a 3 x 3 game between two players X and Y. Xis maximising player and Ythe minimising player.(a) Formulate a suitable Linear Programme model of the game with respect to the minimising player Y and derive the optimal strategy for Y.(b) Write down the dual of
2. A small city with 1,700 customers has three shoe stores S1, S2 and S3• Suppose that due to its location, there are no new customers added and the old ones also do not leave.A survey of the number of customers visiting each store in the past year reveals the following:Using the following
A researcher is analysing switching between two competing products. The shares for the two products are found to be as given here:The researcher believes that an accurate representation of the market share in any period can be obtained by using Markov processes. Assuming his belief is correct:(a)
4. The arrival behaviour of a bank employee reveals that ifhe is late on a day, he is 90 per cent sure to be in-time the next day. Similarly, ifhe is on time on a day, there is a 30 per cent chance that he will be late the next day. How often, in the long run, is he expected to be late for the
5. (a) The purchase patterns of two brands of toothpaste can be expressed as a Markov process with the following probabilities:(i) Which brand appears to have most loyal customers? Explain.(ii) What are the projected market shares for the two brands?(b) Suppose that in part (a) a new toothpaste
Consider the following transition probability matrix:Without making calculations, can you say what would the market share of each of the firms, A, B and C be in equilibrium? Now, verify it by calculations. Here, C is an absorbing state. True? ABC A B C 0.80 0.12 0.08 0.15 0.70 0.15 0 0 1
7. In acitY, only two brands ofcola are sold:AA and BB. If a buyer bought cola AA lasttime, there is 0.75 chance that he would buy the same cola in the next purchase. Similarly, it is known that if a buyer bought brand BB last time, the probability for him to buy the brand AA next time is 0.4.(a)
9. A salesman makes all sales in three cities X, Y and Z only. It is known that he visits each city on a weekly basis and never visits the same city in successive weeks. Ifhe visits city X in a given week, then he visits city Zin the next week. However, ifhevisits city Yor Z, he is twice as likely
8. A researcher is analysing brand switching between different airlines, operating on the Delhi-Mumbai route by frequent fliers. On the basis of the data collected by her, the researcher has developed the following transition probability matrix:It is found that currently the airlines AA, BB and CC
1. What is game theory? State the assumptions underlying it. Discuss its importance to business decisions.
2. Given the following pay-off matrix of a zero-sum game, determine the optimal strategies for the players and the value of the game: A's strategy B's strategy b b b3 b4 a a2 569 2 50 8 -5 7 12 8 7 2 8 -6 5
3. Is the following game strictly determinable? Is it fair? b b b3 b4 bs b6 a 18 8 18 8 18 8 15 6 15 6 15 6 az 18 8 18 8 18 8 -15 -6 -15 -6 -15 -6
4. You are given the paY-offmatrix in respect ofa two-person, zero-sum game, as follows:(a) Write the maximin and minimax strategies.(b) Is it a strictly determinable game?(c) What is the value of the game?(d) Is this game a fair one? B's strategy A's strategy B B B3 B4 B5 A 8 10 -3 -8 -12 A 3 6 0
5. For the following 'two-person, zero-sum' game, find the optimal strategies for the two players and value of the game:If the saddle point exists, determine it using the principle of dominance. Player B B B B3 A 5 9 3 Player A A 6 -12 -11 A3 8 16 10
6. The two major scooter companies oflndia, ABC andXYZ, are competing for a fixed market. Ifboth the manufacturers make major model changes in a year, then their shares of the market do not change.Also, if they both do not make major model changes, their shares of the market remain constant. If ABC
7. The squadron of Sqdn. Leader Kumar is equipped with six Big-27 fighters. The enemy is using X-16 fighters. In combat the two types of planes are matching and they fight to draw if they are in equal numbers. However, if either side uses a larger number of planes, the other side will be destroyed.
8. M/S Godrej & Boyce and Hindustan Lever Ltd. have been selling competing products Cinthol and Liril respectively. The brand manager ofCinthol raised the following question:What should be the firm's strategy in terms ofadvertising for Cinthol? The market Research group of Godrej & Boyce developed
9. A partnership firm with two partners has a net worth of W. Each of the partners owns half of the business and, in addition, has a personal bank account of amount K. Of late, the partners are not on talking terms. Finally, they have agreed through a mediator that one of them would buy other's
10. Two competing firms must open their next branch at one of the three cities: A, Band C, whose distance profile is given here. If both companies open their branches in the same city, they will split the business evenly. If, however, they build the branches in different cities, the company that is
1. Find the saddle point, ifit exists, for each of the following games: (a) b 215 535 -5 b b3 8 2 6 1 3 943 b 552 @
11. How can a 'Two-Person, Zero-Sum Game' problem be converted into a linear programming problem?Illustrate with an example.
2. What do you understand by 'zero-sum' in the context of game theory? Can there be a non-zero-sum game also?
3. 'Game Theory provides a systematic quantitative approach for analysing competitive situations in which the competitors make use oflogical processes and techniques in order to determine an optimal strategy for winning.' Comment.
4. Explain the following:(a) saddle point (b) pure strategy (c) mixed strategy.Give the linear programming equivalent to a Game Theory problem.
5. What is a 'game' in game theory? What are the properties ofa game? Explain the "best strategy" on the basis of minimax criterion ofoptimalitY.
6. Describe the maximin and minimax principles of game theory.
7. Explain with examples the concept of dominance in games theory.
8. "The primary contribution of the game theory has been its concepts rather than its formal application to solving real problems." Explain.
9. "The two-person, zero-sum game is unrealistic." Elucidate the statement bringing out the limitations of game theory, if any.
10. What are the major limitations of game theory?
11. A and B play a game in which each has three coins: a 5 paise, 10 paise and 20 paise coin. Each player selects a coin without the knowledge of the other's choice. If the sum of the coins is an odd amount, A wins B's coin, and if the sum is even, B wins A's coin. Find the best strategy for each
12. Assume that two firms are competing for market share for a particular product. Each firm is considering what promotional strategy to employ for the coming period. Assume that the following paY-off matrix describes the increase in market share for firm A and decrease in market share for firm
13. Two competitors are competing for the market share of the similar product. The paY-off matrix in terms of their advertising plan is as follows:Suggest the optimal strategies for the two competitors and the net outcome thereof. Competitor A's Strategies No Advertising Competitor B's Strategies
25. The effectivity of advertisement in different media by two competitive firms A and Bis given by the paY-offmatrix (in Rs '00) as follows:(i) Test whether there is a saddle point and a pure strategy for optimum returns, with reasons.(ii) Use dominance property to evaluate the mixed strategies of
26. There are two companies A and B in a certain city. Both companies have similar reputation and the total number of customers is equally divided between the two companies. Both the companies want to attract a greater number of customers by using different media of advertisement. BY seeing the
27. Solve the following zero-sum game where player B pays to player A: Player A Player B B B B3 BA B 23 -4 ++ 4 -4 64 -3 5 1 0 A -3
28. Solve graphically the following game: Player A B Player B B 3 4 A A2 -3 12 A3 6 -2 A4 -4 -9 A5 5 -3
29. Consider the following 'two-person, zero-sum' game:Suggest optimal strategies for the two players and the value of the game. Player A's strategies B Player B's strategies B B3 A 6 11 8 A 9 A3 7 58 9 8
30. Firm Xis fighting for its life against the determination of firm Yto drive it out of the industry. FirmX has the choice of increasing price, leaving it unchanged, or lowering it. Firm Y has the same three options. Firm X's gross sales in the event of each of the pairs of choices are shown
31. Convert the following game problem into a linear programming problem. 5 Player A's Strategies 10 Player B's Strategies 7 4 6 2 260 9 0
32. Convert the following game problem, involving 'two-person, zero-sum game' into a linear programming problem:Don't solve. Player B -3 8 20 6 16 2289 Player A 0 4 12 21 -290
33. In respect ofa two-person, zero-sum game, the following paY-offmatrix is given:(a) Show that the above game has no saddle point.(b) Show that the game cannot be reduced by applying dominance rule.(c) Formulate the game as a linear programming problem for player Y and obtain his optimal
24. The following paY-off matrix describes increase in sales of Firm A from each of its strategies A 1, A2, A3, and A4 against each of the strategies B1, B2, B3 and B4 of the rival Firm B.Assuming a zero-sum game, show that no optimal strategy-mix exists in pure strategies irrespective of whether
23. Solve the following game and determine the value of the game also. A's paY-offmatrix is as: b B b b3 a 2 5 6 |A 02 7 3. 4

Showing 1200 - 1300 of 7324

First
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Last

Step by Step Answers

Services

Sitemap
Fun
Definitions
Become Tutor
Used Textbooks
Study Help Categories
Recent Questions
Expert Questions
Campus Wear
Sell Your Books

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship
Online Quiz
Give Feedback, Get Rewards

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Student Discount
Campus Ambassador

Secure Payment

Download Our App

© 2026 SolutionInn. All Rights Reserved