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

9. Ifstatej is reachable from state i, and i is reachable fromj, then i andj are said to be communicative. Mark the statement as T (True) or F (False).
43. The utility function of a manager is as follows:The manager is offered a contract which promises a net gain of Rs 1,00,000 or a net loss of Rs 60,000 with equal probabilities.(a) Should he accept the contract? Use (i) expected monetary value criterion, (ii) expected utility criterion.(b) Would
44. Utility function for money of some decision-maker is as follows:A preference test given to him shows that he is indifferent between an investment that will Yield Rs 10,000 certainly and a risky venture with a 50% chance of Rs 30,000 profit and a 50% chance ofa loss ofRs 1,000.A new risky
45. A manager has following utility function depicting her attitude towards uncertainty:(a) The manager is offered an opportunity with following likely returns along with their respective chances.What is the maximum amount she will be prepared to pay for the opportunity?(b) How would she decide in
46. The utility function of an individual is as given here(a) The individual in question is invited to participate in a contract which can result in a gain of Rs 2 lac or a loss of half this amount with equal probabilities. Show that he would not accept this contract.Now, suppose that there are
36. A car manufacturer, Hindustan Motor Company, in a competitive market, has a plant which can produce 5 models of cars in any desired ratio. The company's profit depends upon the models of cars produced by its competitor, Indian Motor Company, and are given in the following table (the figures are
38. XYZ Company, dealing with a newly invented telephone device, is faced with the problem of selecting out of the following courses of action available:(i) manufacture the device itself; or(ii) be paid on a royalty basis by another manufacturer; or(iii) sell the rights for its invention for a lump
30. Mr Prime, the owner of a chain of facilities manufacturing detergents, is contemplating opening a new facility in a certain area. He usually builds 2,500 tonnes or 5,000 tonnes plants, depending on whether the anticipated demand is low or high. He has been able to construct the following net
32. A company has just received a big lot of electronic components for inspection. Experience indicates that there are only two possible compositions of the lot: D 1 5% defective, or D2 10% defective. Empirical evidence also tells that P(D1) = 0.7 and P(D2) = 0.3. The paY-off matrix for the
33. A company is contemplating the introduction of a new product and is considering the advisability of test marketing done before finally deciding on it. The options on introduction are: to introduce ( call it A1) and not to introduce (call it A2). The management has estimated the following
34. Mr WebbleY, the Marketing Planning Manager of Computer and Allied Co. Ltd. is given the assignment of recommending whether his firm should produce a new type of pocket calculator. His boss feels that a chance of 60:40 exists that the calculator will be successful. The paY-off table in lacs of
35. You are given the following estimates concerning a Research and Development programme:Construct and evaluate the decision tree diagram for the data. Show your working for the evaluation. Decision number, j j = 1: develop j2: do not develop Probability of Outcome decision Dj given Research, R
36. The Unique Candles Company has developed and patented a unique process for manufacturing ornamental candles. The firm has three options: (1) sell the patent, (2) produce and market the product nationally at once, or (3) test market the product in one area and decide either to sell the patent or
37. Portland p.l.c. is planning a new product launch and has to evaluate the following alternatives:(1) To introduce the product in the South-East initially and, after a two-Year period, to evaluate its performance and decide whether to go on a national distribution or remain on a regional
Refer to the detergent example and construct the transition probabilities matrix.The transition probabilities for the problem are given in Table 14.1. TABLE 14.1 Transition Probabilities Matrix From Brand (this month) To Brand (next month) D D2 D3 525 D 0.60 0.30 0.10 D 0.20 0.50 0.30 D3 0.15 0.05
Obtain the transition matrix for the gambler's ruin problem discussed earlier.From the given information, it can be seen that there are five states viz. Rs 0, Rs 10, Rs 20, Rs 30, and Rs 40. From all the states, except the states of Rs O and Rs 40, we know that the person would be in the next state
1. Markov chains exemplitY stochastic processes. Mark the statement as T (True) or F (False).
2. Like other operations research tools, such as linear programming, the Markovian analysis is used to determine the optimal course of action in a given problem. Mark the statement as T (True) or F (False).
3. Markovian analysis deals with those situations which involve multiple time periods. Mark the statement as T (True) or F (False).
4. In a discrete stochastic process, the state of the system can be viewed at any point in time. Mark the statement as T (True) or F (False).
5. Black and Scholes' formula for valuation of options is based on the assumption of viewing the share prices as a continuous-time stochastic process. Mark the statement as T (True) or F (False).
6. A transition probability matrix indicates the probabilities of inter-state moving. Mark the statement as T (True) or F (False).
7. Homogeneous Markov chains are based on the assumption of constancy of transition probabilities. Mark the statement as T (True) or F (False).
8. A sequence of transitions beginning in state i and ending in statej is called a transition from i toj. Mark the statement as T (True) or F (False).
A manufacturing company has two production departments, designated below as P1 and P2, and three service departments, designated below as S1, S2 and S3, and wishes to allocate all factory overhead to production departments. A primary distribution of overhead to all departments has been made and is
ABC Hospital operates on a charity basis. All expenses are paid for by the government.Recently, the board of governors of the hospital has been complaining about the size of the budget and insisting that the hospital cut expenses. The major area of concern has been the cost of keeping patients in
Consider the accounts receivable problem of a firm. Suppose that, for this firm, an accounts receivable turns into bad debt if the account is more than three months overdue. Now, at the beginning of each month, each of the accounts may be classified into one of the following states:State 1 : New
market survey is made on two brands of breakfast foods A and B. Every time a customer purchases, he may buy the same brand or switch to another brand. The transition matrix is given below:At present, it is estimated that 60 per cent of the people buy brand A and 40 per cent buy brand B. Determine
In a certain market, only two brands of lipsticks, A and B, are sold. Given that a lady last purchased lipstick A, there is 80% chance that she would buy the same brand in the next purchase, while if a lady purchased brand B, there is 90% chance that her next purchase would be brand B. Using this
Consider the following transition probability matrix:You are required to (i) provide an example of path in this;(ii) give an example of states which communicate;(iii) provide an example of recurrent state;(iv) provide an example of transient state; and (v) identify if there exists an absorbing
Recently, a market research team has conducted a survey of consumer buying habits with respect to three brands of talcum powder in an area. It estimates that, at present, 20 per cent of the customers buy brand A, 50 per cent of the customers buy brand Band 30 per cent of them buy brand C. In
A housewife buys three kinds of cereals C1, C2 and C3. It is known that she never buys the same cereal on successive weeks. If she buys cereal C1, then the next week she buys cereal C2. However, if she buys C2 or C3, then the next week she is thrice as likely to buy C1 as the other brand.Obtain the
To investigate brand switching between different brands of detergent powder, a research company surveyed shoppers in an area to discover their behaviour. The survey on a number of shoppers in relation to three leading brands Superwash, Clean and Shine has revealed the following information.(a)
Suppose that new razor blades were introduced in the market by three companies at the same time. When they were introduced, each company had an equal share of the market, but during the first year the following changes took place:(i) Company A retained 90 per cent of its customers, lost 3 per cent
29. The Good-neighbours' Apartment has eight washing machines. The probability of machines failing in any given Year is as follows:Once a machine has failed, its repair will cost either Rs 30, the minimum service charge; Rs 70 for a moderate repair, or Rs 120 for a major repair. The chance for a
28. Z Ltd. is considering various product pricing and material purchasing options with regard to a new product it has developed. Estimates of demand and costs are as follows:Each unit requires 3 kg of material and because of shortage problems any unused material must be sold at Re 1 per kg. The
1. The research department of Hindustan Lever has recommended the marketing department to launch a shampoo of three different types. The marketing manager has to decide one of the types of shampoo to be launched under the following estimated pay-offs (in millions of Rs) for various levels of
2. A toy company is bringing out a new type oftoY. The company is attempting to decide whether to bring out a full, partial or minimal product line. The company has three levels of product acceptance. The management will make its decision on the basis of expected profit from the first Year of
3. The oil company oflndia is interested in acquiring a piece ofland which is considered likely to contain oil deposits. The company has the option of(a) buying the land outright, (b) obtaining an option to buy, drill for oil and if found exercise the option, and (c) not buying or obtaining option.
4. A firm is considering the purchase of a complex equipment from either of the two suppliers S1 and S2•Supplier S1 is capable of supplying the equipment on time to meet a certain desired deadline. The price chargeable by S1 is, however, considerably higher than that of S2• It is felt by the
5. (a) From the following matrix, the elements of which indicate profits, obtain the decisions using the following principles of decision-making:(i) Maximax (ii) Maximin (iii) Laplace(b) How would your answer in (a) be different if the elements of the matrix represented costs? a a2 as as 26 22 13
6. Find the best alternative in the following decision table using expected value criterion and the criterion of expected regret. The entries in the matrix indicate profits associated with different combinations of acts and states of nature. State of nature (Q) Prob. Act a Act a Act a3 0.6 0 3 -3
8. Three types of souvenirs can be sold outside a stadium. From the following conditional paY-offtable, construct the opportunity loss table. (Sales are dependent on the winning team.)Point out which type of souvenir should be bought if probability of Team A's winning is 0.6. I (Rs) Team A wins
9. Chemical Products Ltd. produces a compound which must be sold within the month it is produced, if the normal price of Rs 100 per drum is to be obtained. Anything unsold in that month is sold in a different market for Rs 20 per drum. The variable cost is Rs 55 per drum.During the last three
20. A television dealer finds that the cost of a TV in stock for a week is Rs 30 and the cost of a unit shortage is Rs 70. For one particular model of television the probability distribution of weekly sales is as follows:How many units per week should the dealer order? Also, find EVPI. Weekly
23. A mineral processing company wants to decide about the number of spare gear trains it has to order out at the time of placing order, for a high horsepower gearbox connected to a grinding unit. Although the life of a gear can be as high as 30 years and more, sudden failures cannot be ruled out.
24. A national boutique chain sells a wide range of high quality customised fashion goods. One particular outfit is bought in at Rs 80 and sold at Rs 130. Mean holding costs per season per outfit work out at Rs 5 and it costs Rs 800 to order and receive goods into stock. The manufacturers require
25. The manager of the boutique has to decide how many luxury gift packs of cosmetics to buy for the forthcoming Diwali season. The gift packs have to be bought from a manufacturer in cases of 50. The profit per pack is Rs 20. On the basis of trading conditions last Diwali, the current economic
26. Using the following pay-off function, develop a paY-offmatrix and determine the optimal policy.M(a;,d) indicates the pay-off associated with ith act andjth state of nature (400d 300 (adj) if if a; > dj aj s dj M(a, d=400a i3, 4, 8; j 3, 4, ..., 6
27. Jackston, Inc. manufactures and distributes a line of Christmas toys. The company had neglected to keep its doll house line current. As a result, sales decreased to approximately 10,000 units per year from a previous high of 50,000 units. The doll house has been redesigned recently and is
19. Company B has ordered a special purpose generator from BHEL at a cost of Rs 90 million. A critical component in the generator is subject to random failure as per probability pattern shown below. If a spare is ordered along with the order for the generator, the cost per component will be Rs 5
10. For the past 200 days, the sales of bread from the Fresh Food Bakery have been as follows(a) Determine the expected sales of bread.(b) The bakery's production costs are Rs 2 per loaf, sale price is Rs 4 per loaf, and any bread unsold at the end of the day is contracted to a local farmer who
11. A physician purchases a particular vaccine on Monday of each week. The vaccine must be used within the week following, otherwise it becomes worthless. The vaccine costs Rs 20 per dose and the physician charges Rs 60 per dose. In the past 50 weeks, the physician has administered the vaccine in
12. A merchant buys a certain item for Rs 20 per case and sells it for Rs 50 per case. The high mark-up reflects the probability of the item and the great risk in stocking it. Any unsold items must be scrapped at the end of the day and have no salvage value. The merchant wants to know how many
42. Lots of a complicated machine part are obtained from a manufacturer. They may be tested only by actually using a sample of a few pieces. Suppose that it is known that the parts are produced by a process which turns out either a 10% defectives or 4% defectives. Suppose further that it is agreed
41. The Dragon Group owns a large store in Mumbai, which is rather old-fashioned and has declining profits.The management of the company is considering some options, and three possibilities worked out:(i) Shut down and sell the site for Rs 15 million.(ii) Continue as before with profits declining
40. B&L Inc. has been invited to bid on a government contract for a lens system for a satellite camera.B&L management estimates the cost of preparing a bid will be Rs 500,000. They also estimate that if they bid on this contract, there is a 60 per cent chance that they will win the contract. The
39. A company is currently working with a process, which, after paying for materials, labour and so on brings a profit of Rs 12,000. The company has the following alternatives:(i) The company can conduct research R1 which is expected to cost Rs 10,000 and having 90%probability of success. If
31. A company receives shipments of certain items. It should decide whether to accept or reject the shipment, on the basis of inspection of a sample selected from the shipment. From the past experience, it is known thatthe percentage of defective items in a batch of shipment is either 1, 2 or 5,
22. The XYZ company has total excess cash funds of Rs 60,000 to invest in various projects during this month and the next, according to the cash-flow statement prepared by the accounting department. The firm has been offered the following investment opportunities. It can participate immediately (at
21. A company has a patent on a new medical device selling for Rs 28 per unit. However, the demand for the device is uncertain. The company can build its own manufacturing facilities and incur fixed cost of Rs 24 lacs per annum and a variable cost of Rs 8 per unit. On the other hand, the company
18. A man has the choice of running either a hot snack stall or an ice cream stall at a sea-side resort during the summer season. Ifit is a fairly cool summer, he should make Rs 5,000 by running the hot snack stall, but if the summer is quite hot he can only expect to make Rs 1,000. On the other
14. A businessman has Rs 10,00,000 available to invest. He can either put the money in the bank at six per cent interest or he can start a new business venture. For the second act, he expects to make 12 per cent return on his investment if the business is a success, but if the business is a
13. The manufacturer of designer jeans must decide whether to build a large factory or a small factory in a particular location. The profit per pair of jeans manufactured is estimated as Rs 10. A small factory will have an amortised annual cost of Rs 200,000 with a production capacity of 50,000
7. A dealer in second-hand machinery is offered 5 machines by a company for Rs 5,000 only. He expects to sell each of the machines for Rs 2,200 at a fair but he also knows that any machines not sold would be a waste and not fetch anything later on. Obtain the paY-off matrix under each of the
8. What is the significance of utility as a basis of decision-making? State the assumptions underlying the theory ofutility.
7. What are decision trees? How and in what type of situations are they employed for decision-making?
6. Explain the posterior analysis of decision-making. Define the expected value of sample information.Give a measure of efficiency ofEVSI.
5. Define EVPI. How is it calculated?
4. (a) How are maximum likelihood and expectation principles of choice differentiated?(b) Do the principles of minimisation of expected cost and minimisation of expected regret Yield the same decision?
3. Explain and illustrate the following principles of decision-making:(a) Laplace, (b) Maximin, (c) Maximax, (d) Hurwicz, (e) Savage, and (t) Expectation.
2. What are paY-off and regret functions? How can entries in a regret table be derived from a paY-offtable?
1. Describe the steps involved in the process of decision-making.
30. A given utility function holds for a given individual at a given point in time only. Mark the statement as T (True) or F (False).
2 9. For any utility function, the utils, the units of measuring utility, should always range between zero and 100. Mark the statement as T (True) or F (False).
28. The expected utility and expected monetary value criteria would always Yield same optimal solution in any given problem. Mark the statement as T (True) or F (False).
27. A risk-averse individual is always willing to accept a smaller cash-certain amount than the expected value of a bet. Mark the statement as T (True) or F (False).
26. The utility approach considers expected utility, rather than expected monetary value as the criterion of decision making. Mark the statement as T (True) or F (False).
25. A decision taken on the basis of expected monetary value would always prove to be the right decision. Mark the statement as T (True) or F (False).
24. The probabilities of various outcomes at each chance node should always add up to one. Mark the statement as T (True) or F (False).
23. The rollback technique of analysing decision trees involves working through it from right to left, evaluating the best course of action at later stages so as to decide on such action at the earlier stages. Mark the statement as T (True) or F (False).
22. In decision trees, the probabilities of all events at chance nodes and the monetary evaluations of different alternatives must all be known in advance. Mark the statement as T (True) or F (False).
21. In a given situation, do nothing can also be the best course of action. Mark the statement as T (True) or F (False).
20. In the decision trees, no more than two alternative courses of action can emanate from a decision node. Mark the statement as T (True) or F (False).
19. The decision tree approach to decision-making is appropriate in those situations where a sequence of decisions are involved. Mark the statement as T (True) or F (False).
18. Efficiency index is the ratio of expected value of sample information to expected value of perfect information. Mark the statement as T (True) or F (False).
17. Expected value of sample information is equal to expected cost with sample information minus expected cost without sample information. Mark the statement as T (True) or F (False).
16. Posterior probabilities are obtained by moditYing prior probabilities taking into consideration the information from a sample. Mark the statement as T (True) or F (False).
15. In Bayesian approach to decision making, the optimal strategy is determined using posterior probabilities. Mark the statement as T (True) or F (False).
14. For each strategy in a given case, the following would hold:Expected paY-off + Expected regret= a constant (EPPI) Mark the statement as T (True) or F (False).
13. EVPI is the expected regret value of any strategy. Mark the statement as T (True) or F (False).
12. EPPI is the expected paY-offunder certainty. Mark the statement as T (True) or F (False).
11. All criteria for decisions under risk inherently assume that the particular ( optimal) decision reached will be repeated a large number of times. Mark the statement as T (True) or F (False).
10. Expected paY-off and expected regret criteria would both lead to identical decisions in a given case. Mark the statement as T (True) or F (False).
9. Maximum likelihood principle is expected to Yield good decisions when the probability of a particular event is predominantly larger in relation to probabilities of other events. Mark the statement as T (True) or F (False).
8. In case ofpaY-offs represented as profits, the Savage criterion for selecting optimal course of action will be based on the maximin principle. Mark the statement as T (True) or F (False).
7. In situations of decisions under uncertainty, the Laplace criterion is the least conservative while the minimax criterion is the most conservative. Mark the statement as T (True) or F (False).
6. In Hurwicz criterion, the maximum paY-off is multiplied by a and the minimum by 1 -a, where a may be any number between zero and 100. Mark the statement as T (True) or F (False).
5. Minimax is an optimist's choice while Minimin is a pessimist's criterion. Mark the statement as T (True) or F (False).
4. Laplace principle is based on the premise of equal probability of occurrence of possible events. Mark the statement as T (True) or F (False).

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