Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech III QUANTITATIVE ANALYSIS FOR BUSINESS DECISIONS Previous Question Paper (August - 2022 - R18)
Answer any five questions. All questions carry equal marks.
Main
What is a model? How model building is the essence of operations research problem?
Answer
A model is a simplified representation of a real-world system or process, designed to capture the essential characteristics and relationships of the system while abstracting away unnecessary complexities. In operations research, models are mathematical or logical frameworks used to analyze, predict, and optimize decision-making processes.
Model building is the essence of operations research because it transforms a complex, unstructured managerial problem into a structured mathematical format. This process involves:
- Problem Definition: Identifying the objective, constraints, and decision variables.
- Abstraction: Translating real-world variables into mathematical symbols and equations.
- Validation: Ensuring the model accurately reflects the reality of the situation.
- Optimization: Using mathematical techniques to find the best possible solution within the defined constraints.
By building a model, the decision-maker can experiment with different scenarios in a controlled environment, leading to objective, data-driven decisions that would be difficult or impossible to achieve through intuition alone.
What is meant by a feasible solution of an LP problem?
Answer
A feasible solution of a Linear Programming (LP) problem is any set of values for the decision variables that satisfies all the given constraints of the problem simultaneously, including the non-negativity restrictions.
In a graphical representation, the feasible solution corresponds to any point located within or on the boundary of the feasible region. The feasible region is formed by the intersection of all half-planes defined by the constraints. If a set of values violates even one constraint, it is considered an infeasible solution. The objective of an LP problem is to identify the optimal solution, which is the specific feasible solution that maximizes or minimizes the objective function.
A company produces two types of presentation goods A and B that require gold and silver. Each unit of type A requires 3 mg of silver and 1 mg of gold while B requires 1 mg of silver and 2 mg of gold. The company can produce 9 mg of silver and 8 mg of gold. If each unit of type A brings a profit of Rs.40 and that of type B Rs.50, determine the number of units of each type that should be produced to maximize the profit.
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Write brief on various phases of developing a model.
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A company has three warehouses A, B and C and four stores W, X, Y and Z. The warehouses have altogether a surplus of 150 units of a given commodity as follows: A 50, B 60, C 40. The four stores need the following amounts: W 20, X 70, Y 50, Z 10. Cost in Rs. of shipping one unit of commodity from various warehouses to different stores is as follows:
| Warehouse / Store | W | X | Y | Z |
|---|---|---|---|---|
| A | 50 | 150 | 70 | 60 |
| B | 80 | 70 | 90 | 10 |
| C | 15 | 87 | 79 | 81 |
Find the optimum distribution schedule and the associated transportation cost.
Answer
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In textile sales emporium four salesmen A, B, C and D are available to four counters W, X, Y, Z. Each salesman can handle any counter. The service time (in hour) of each counter when manned by each salesman is given below:
| Salesman / Counter | W | X | Y | Z |
|---|---|---|---|---|
| A | 41 | 72 | 39 | 52 |
| B | 22 | 29 | 49 | 65 |
| C | 27 | 39 | 60 | 51 |
| D | 45 | 50 | 48 | 52 |
How should be the salesmen allocated to counters so as to minimize the service time? Each salesman must handle only one counter.
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The initial cost of a machine is Rs.3,00,000 and running or operating expenditure which increases with age of the machine is given below:
| Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Running cost (Rs) | 50,000 | 60,000 | 80,000 | 1,00,000 | 1,30,000 | 1,60,000 | 2,00,000 |
What is replacement policy? When this machine should be replaced? It is given that the rate of interest is 10% per year, the discounted factor over a period of one year is given by 0.909, 2 years 0.826, 3 years 0.751, 4 years 0.683, 5 years 0.621 and six years 0.564.
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The cost of a machine is Rs.6,10,000 and its scrap value is Rs.10,000. The maintenance costs found from experience are as follows: Year 1: 10,000, Year 2: 25,000, Year 3: 40,000, Year 4: 60,000, Year 5: 90,000, Year 6: 1,20,000, Year 7: 1,60,000. When should the machine be replaced?
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Examine the procedure for group replacement of low cost items in a manufacturing firm.
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Briefly explain the following decision criteria: i) Maximax or Minimin and Maximin or Minimax ii) Criterion of realism and Criterion of regret.
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Consider the following game with the following payoff table:
| Player/Player | B1 | B2 | B3 | B4 |
|---|---|---|---|---|
| A1 | -5 | 3 | 1 | 10 |
| A2 | 5 | 5 | 4 | 6 |
| A3 | 4 | -2 | 0 | -5 |
Solve the above game, giving the strategy selection for each player and value of the game.
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A departmental store has a single cashier. During the rush hours, customers arrive at the rate of 20 customers per hour. The average number of customers that can be processed by the cashier is 24 per hour. Assume that the conditions for use of the single channel queuing model apply.
a) What is the probability that the cashier is idle?
b) What is the average number of customers in the queuing system?
c) What is the average time a customer spends in the system?
d) What is the average number of customers in the queue?
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