JNTU
JNTU B.Tech III QUANTITATIVE ANALYSIS FOR BUSINESS DECISIONS Previous Question Paper (February - 2023 - R18)
Note: i) Question paper consists of Part A, Part B. ii) Part A is compulsory, which carries 25 marks. In Part A, Answer all questions. iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.
PART - A
What are the advantages and limitations of Linear Programming models?
Answer
Linear Programming (LP) models offer several advantages and limitations in business decision-making:
Advantages:
- Provides an objective, systematic, and scientific approach to resource allocation, ensuring optimal utilization of scarce resources.
- Helps management identify potential bottlenecks and evaluate the impact of changing constraints through sensitivity analysis.
Limitations:
- Assumes linear relationships between variables, which may not accurately reflect real-world scenarios involving economies of scale or non-linear costs.
- Requires all parameters (coefficients) to be known with certainty, failing to account for the inherent risks and uncertainties present in dynamic business environments.
Explain what is meant by “shadow price of the resource” in the context of duality.
Answer
In linear programming, the shadow price of a resource represents the rate of change in the optimal value of the objective function per unit increase in the availability of that resource, assuming all other parameters remain constant. It is formally defined as the dual variable value associated with a specific constraint in the optimal solution.
Key points include:
- It indicates the maximum amount a decision-maker should be willing to pay for an additional unit of a scarce resource.
- If a resource is not fully utilized (i.e., there is slack), its shadow price is zero because an increase in its availability does not improve the objective function.
- It provides a measure of the sensitivity of the optimal solution to changes in the right-hand side values of the constraints.
What is assignment Problem? Give two areas of its applications.
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Give the mathematical formulation of transportation problem.
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How would you deal with replacement of items that fail completely and suddenly?
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What is the difference between group replacement and individual replacement? Under which circumstances group replacement may become profitable?
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How is the concept of dominance used in simplifying the solution of rectangular games?
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Explain the difference between expected opportunity loss and expected value of perfect information.
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What happens to the Queue when arrival frequency is more than servicing frequency?
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What are the advantages and disadvantages of simulation models?
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PART - B
Discuss the assumptions in Linear Programming Problem.
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Min z = x1-3x2+2x3, subject to 3x1-x2+3x3≤ 7, -2x1+4x2≤12, -4x1+3x2+8x3≤10 and x1, x2, x3 ≥0.
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Maximize z=4x1+5x2-3x3+50, subject to the constraints, x1+x2+x3=10, x1-x2≥1, 2x1+3x2+x3≤40, x1, x2, x3≥0.
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Goods have to be transported from factories F1, F2, F3 to ware-houses W1, W2, W3 and W4. The transportation cost per unit, capacities and requirements of the warehouse are given in the table. Find the distribution with minimum cost.
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Five men are available to do five different jobs. From past records, the time (in hours) that each man takes to do each job is known. Find the assignment of men to jobs that will minimize the total time taken.
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A firm has a machine whose purchase price is Rs.20, 000. Its maintenance cost and resale price at the end of different years is given. a) Obtain the economic life of machine and the minimum average cost. b) The firm has obtained a contract to supply the goods produced by the machine, for a period of 5 years from now. If the firm has a machine of this type that is one year old, what replacement policy should it adopt if it intends to replace the machine more than once?
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A large TV manufacturer has to provide “Service after sales” on annual contract basis. The company has now 500 TV sets; and has to decide on service policy. Service is restricted to replacement of minor parts. The failure pattern is given. Which policy would you recommend: a) Replace as and when minor parts fail. b) Replace at periodic intervals, say at the end of one month/two months etc?
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Solve the following game using graphical approach.
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A TV dealer finds that the cost of holding a TV in stock for a week is Rs.50. Customers who cannot obtain new TVs immediately tend to go to other dealers and he estimates that for every customer who cannot get immediate delivery he loses an average of Rs.200. The probabilities of selling 0, 1, 2, 3, 4 and 5 TVs in a week are 0.05, 0.10, 0.20, 0.30, 0.20 and 0.15 respectively. a) How many televisions per week should the dealer order? b) Compute EVPI. c) The dealer is thinking of spending on a small market survey, how much should he be willing to spend?
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A commercial bank has two tellers working on savings accounts. The first teller handles withdrawals only. The second teller handles deposits only. It has been found that service time distributions for both deposits and withdrawals are exponential with mean service time are 3 minutes per customer. Depositors are found to arrive in a Poisson fashion throughout the day with mean arrival rate of 16 per hour. Withdrawers also arrive in a Poisson fashion with mean arrival rate of 14 per hour. What would be the effect on the average waiting time for depositors and withdrawers if each teller handles both withdrawals and deposits?
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A company manufactures around 150 two wheelers. The daily production varies from 146 to 154. The finished two wheelers are transported in a specially arranged vehicle accommodating only 150 two wheelers. Using the provided random numbers, simulate the process to find on: a) What will be the average number of two wheelers waiting in the factory? b) What will be the average number of empty spaces on the specially designed vehicle?
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